Oct 292015
(definition LG5DEF) of (definition LG5DEF) LG5QVP, ‘this site's documentation for its users’, definition LG5DEF Add comments
^{NWYUYU} ‘intro & overall’
 ^{NWZ059} ‘This {post & its comments}’s ‘TOU(Terms Of Use) including copyright ©, confidentiality/privacy, & info’s allowed use’ is JotHere.com’s default TOU(Terms Of Use) except:’ none.

.
^{NWZ0V8} post name & ‘post image’:
‘‘constructing: {‘NOLDef’ {‘weighted graph’ & related}} ‘in ‘NOLDef’’ ’NWYUYU’
 ^{NWZ0VS} ‘‘section history additional’ ‘in reverse start order’:’
 ^{NXKHDI} present
 ^{NXKHFI} follow /4670#NXK0JA plus fix the link
 ^{NX2XMJ} ‘‘constructing: ‘‘‘definition in ‘NOLDef’ ..’..’’ of {‘NOLDef’ {‘weighted graph’ & related}} ’NWYUYU’
 ^{NX3OQE} ‘ & similar’ ‘replacement’ ‘& related’
 ^{NX2XSX} more accurate with new wording
 ^{NX2XS4} cut ‘concepts’ as just too much here
 ^{NWZ0W6} ‘‘constructing: ‘‘‘definition in ‘NOLDef’ of concept’s’’ of {‘NOLDef’ {partial order relations & similar}} ’NWYUYU’
 ^{NWZ0WQ} ‘so post category’
 ^{NWZ836} ‘NOLDef NWZ578’
 ^{NWZ7QW} ‘this site’s documentation for its users NQBFBL’ –as implied but not yet in practice
 ^{NWZ84P} ‘in NOLDef NWZ6UN’
 ^{NWZ836} ‘NOLDef NWZ578’
 ^{NXKHDI} present
 ^{NWZ0VS} ‘‘section history additional’ ‘in reverse start order’:’
 ^{NWZ05J} ‘To reply & discuss, please use JotHere.com’s default methods (click) except:’ none.
 ^{NWZ060} ‘for remainder, sections overall’ ‘definition’ + TBA+ ‘contributors’ + ‘post history additional’
 ^{NWZ067} ‘‘‘definition in ‘NOLDef’ of concept’s’’ of…: ‘‘definition in ‘NOLDef’ of concept’s’
 ^{NYIQHC:} ‘’ ‘‘operation/phrase’’
 ^{NYJFHE:} ‘usage’
 ^{NYJFHP:} top
 ^{NYJFK4:} as language, including mathematics & all others, seemingly can’t exist without it, as no meaningful expressions can be made.
 ^{NYJG1B:} so IMHO should be taught to everyone ASAP
 ^{NYJG2C:} as, for math, right after teaching ones 1st 2 to 4 ‘operator’/operations (typically standard arthimetic, so add, multiply, etc)
 ^{NYJHK9:} so around 4th grade.
 ^{NYJG2C:} as, for math, right after teaching ones 1st 2 to 4 ‘operator’/operations (typically standard arthimetic, so add, multiply, etc)
 ^{NYJFHP:} top
 ^{NYIRM2:} ‘‘definition’ ‘anew’’
 ^{NYIS1I:} a connection
 ^{NYJ92A:} which, if utilized to unify particular instances of its values, is a calculation
 ^{NYJ87T:} between its values
 ^{NYJ9R9:} where each which can be, and mostly is, {particular, meaning used as a component of other operation(s) and/or be 1 constant}
 ^{NYJA10:} of type
 ^{NYJ8A2:} the ‘operator’ with
 ^{NYJA9I:} the quantity being 1
 ^{NYJ8D2:} the operand(s), with
 ^{NYJA7O:} the quanity is the arity
 ^{NYJBRV:} the domain of each operand, taken together, is the domains
 ^{NYJA80:} the collective possible values, specificaly the cartesian product of the domains, is the domain
 ^{NYJ9MA:} the output/result/value(term source) aka meaning(term source), with
 ^{NYJAAP:} the quantity being 1
 ^{NYJGWF:} the values possible or constrained to the range
 ^{NYJAPY:} the values possible is the image, with
 ^{NYJCV6:} a certain superset is the codomain
 ^{NYJCWO:} which is {the 1st or last of the domains} typically, including for ‘operation on 1 set’
 ^{NYJCV6:} a certain superset is the codomain
 ^{NYJH5P:} the image else the codomain is the range
 ^{NYJH7J:} so, because the terms’s ambiguity, seemingly a term to avoid
 ^{NYJ8A2:} the ‘operator’ with
 ^{NYJ9HZ:} called the operator being applied to these operands or the application of the operator to the operands
 ^{NYIS1I:} a connection
 ^{NYIR98: }‘per def’ ‘same or similar’ ‘sub’
 <0
 ^{NYJIDS:} 0 ‘Wikipedia’
 ^{NYIQIL: }https://en.wikipedia.org/wiki/Operation_(mathematics) especially https://en.wikipedia.org/wiki/Operation_(mathematics)#General_description except
 ^{NYJBE4:} presently every defintion of meaning (there & on that article & often on related articles, plus on all other instructional texts I recall)
 ^{NYJFNT:} is weak
 ^{NYJFUQ:} why?
 ^{NYJHQB:} my guess is (similar reasons)
 ^{NYJFV5:} because it’s so incredibly basic, as perhaps like walking, those who really get it then don’t want to bother to stop & explain it.
 ^{NYJHPQ:} because we don’t teach it early, by the time someone finally gets it, because it’s so incredibly basic so far back, then few want want to go back that far and explain it, creating a nasty catch22.
 ^{NYJHQB:} my guess is (similar reasons)
 ^{NYJFP1:} which given top use, is terrible IMHO
 ^{NYJFXB:} including causing even me, a top MIT CS grad
 ^{NYJGR2:} suffering from the ‘range’ meaning‘s confusion until just now writing that point!
 ^{NYJGQH:} not to really start seeing & getting all these concepts until midway thru college
 ^{NYJGAF:} until being introduced to such abstractions by my personal study of symbolic computation plus the MIT CS courses
 ^{NYJHEY:} when instead IMHO ~4th grade seems appropriate for me & most to be taught this
 ^{NYJFXB:} including causing even me, a top MIT CS grad
 ^{NYJFO6:} specifically from most problematic,
 ^{NYJHH9:} does not seem to emphasize its top importance
 ^{NYJBB4:} is missing, often notably, all the core related components, for instance
 ^{NYIRTA:} ‘a calculation from zero or more input values (called “operands“) to an output value’ is missing ‘operator’ , general arity, domain, codomain, etc.
 ^{NYJC1U:} is not a nicelybroken down outline, which, IMHO, is dramatically more readable & usable.
 ^{NYJ9DV:} ‘calculation’ should be replaced with ‘connection’ per distinction #NYJ92A
 ^{NYIRSD:} ‘An operation ω ’ should be ‘An operator ω’
 ^{NYJBKV:} sometimes gives detail that instead belongs in the the defintion of subcomponents, for instance
 ^{NYJBNZ:} ‘power of the codomain’ belongs in my ‘operation on 1 set’
 ^{NYJFUQ:} why?
 ^{NYJFNT:} is weak
 ^{NYJBE4:} presently every defintion of meaning (there & on that article & often on related articles, plus on all other instructional texts I recall)
 ^{NYJIEB:} https://en.wikipedia.org/wiki/Phrase
 ^{NYIQIL: }https://en.wikipedia.org/wiki/Operation_(mathematics) especially https://en.wikipedia.org/wiki/Operation_(mathematics)#General_description except
 ^{NYJI4Y: } ‘‘name’ ‘anew’’
 ^{NYJIDG:} ‘operation/phrase’
 ^{NYJLT1:} ‘‘rendering’ ‘anew’’ ‘‘operation/phrase’’
 ^{NYJI8T:} ‘operation’ –starting at concept’s id time
 ^{NYJIDG:} ‘operation/phrase’
 ^{NYJLMA: }‘‘‘Pretty Link’ entry’ ‘anew’’ section 1st
 ‘for remainder, sections overall’
 ^{NYIRMG:} is represented by an expression of form…
 ^{NYJDZ8:} _ (name TBA)
 ^{NYJE08:} the by far most typical (form), at least for human consumption
 ^{NYJDX4:} gives only & all the operation’s components except
 ^{NYJD7X:} the expression itself stands for the result
 ^{NYJE19:} a tuple/row consisting of a primary id, plus a foreign id (referencing another or this such id) for each of {the values including the result}
 ^{NYJE7L:} a number of others possible
 ^{NYJDZ8:} _ (name TBA)
 ^{NYJUH0: }‘’ ‘‘‘operation/phrase’ ‘default connections’’’ (aka ‘precidence’)
 ^{NYJRH3: } ‘usage’
 ^{NYJRHC: }never else minimally relying on defaults here
 ^{NYJRJV:} is so far NOT the norm in popular communications
 ^{NYJVUB:} is done by…
 ^{NYJVTB:} programming language
 is done by data langauge
 ^{NYJVGY:} is done by XML so potentially all HTML
 ^{NYJVKL:} somewhat unobviously: because parantheticals are done not by ‘(..)’ or other familar equivalents, but by done ‘<tag ..>..</tag>’ so not using pathethesis per se, so perhaps per that, sneaking into acceptance as likely required)
 ^{ }

 ^{NYJVNG:} which is extremely {famous & proven}
 ^{NYJRMD:} I recommend
 ^{NYJROF:} with the minimal exception of
 ^{NYJS1F:} {method call/memberaccess} is leftassociative
 ^{NYJS4H:} as in many cases here #NYJS0T would not hold, including
 ^{NYJS6Z:} including for pure functional results in near infinite parenthesization, including infinte if interactivity added
 ^{NYJS4H:} as in many cases here #NYJS0T would not hold, including
 ^{NYJT76:} possibly (low) a few others I’ve not yet conceived.
 ^{NYJS1F:} {method call/memberaccess} is leftassociative
 ^{NYJSAB:} as, from biggest reasons:
 ^{NYJSEZ:} clarity should always be preferred whenever practical (which it is), including
 ^{NYJSIF:} such defaults are complex and often not well understood (plus we may want to change), so bugs & misunderstandings are commonly introduced
 ^{NYJU20: }the number of parentheticals then requiring addition which one would typically otherwise skip/save, is quite managable, including:
 ^{NYJS0T:} small, usually no more than ~5 levels, so a small constant addition.
 ^{NYJSB7:} with any respectable text editor & viewer (so providing good paren matching & jumping), as Brackets and most famously emacs, properly makes matching is easy plus has power features
 ^{NYJSM6:} my guess is the lack of such editors & viewers being commonplace is the biggest reason such for the present norm even for languages we’ve developed in recent history.
 ^{NYJV3U:} makes language parsing dramatically simpler
 ^{NYJV4L:} significantly enabling helpful syntactic tools, as example
 ^{NYJV83:} readily enables powerful editor & viewer features as expression jumping & especially code folding
 ^{NYJVAJ:} significantly encouraging the development of custom languages by demonstrating one doesn’t don’t need a fancy parser to have a a new powerful programming/expression language
 ^{NYJTU6:} only a few languages allow custom (operators, here called functions or similar) to have precidence
 ^{NYJTWO:} by overloading the builtin operators with no change in their precidence (so same parser works)
 ^{NYJTXK:} feels like the norm
 ^{NYJT9A:} customizing/overriding these defaults, so customizing precidence, appears hard (requring an advanced parser) & rare
 ^{NYJU5T:} Mathematica seems to have it per Q&A
 ^{NYJTRG:} F# may have it per article
 ^{NYJTJY:} Perl 6 may have it; possible example
 ^{NYJTTH:} relevant discussion http://mortoray.com/2012/07/13/cantheideallanguageallowscustomoperators/
 ^{NYJTWO:} by overloading the builtin operators with no change in their precidence (so same parser works)
 ^{NYJV4L:} significantly enabling helpful syntactic tools, as example
 ^{NYJSEZ:} clarity should always be preferred whenever practical (which it is), including
 ^{NYJROF:} with the minimal exception of
 ^{NYJRHC: }never else minimally relying on defaults here
 ^{NYJQ2H: }‘‘definition’ ‘anew’’
 ^{NYJQ2Q:} rule(s) telling what operation(s) connections to make by default when this info is not specified by an operation(s) expression.
 ^{NYJQEO:} especially telling, for each ‘operator’ (given else implied) by the expression, which of the expression’s other values, including result values & possibly implied values, are to be its operands
 ^{NYJQZQ:} which in most potentially all cases means what {parentheses groups (to denote ‘precidence’ as that that link details) plus possibly its operand(s)} are to be inserted into the expression to correct, hopefully fully, for it here being incomplete else shorthanded.
 ^{NYJQEO:} especially telling, for each ‘operator’ (given else implied) by the expression, which of the expression’s other values, including result values & possibly implied values, are to be its operands
 ^{NYJQ2Q:} rule(s) telling what operation(s) connections to make by default when this info is not specified by an operation(s) expression.
 ^{NYJUYO: }‘per def’ ‘same or similar’ ‘sub’
 <0
 ^{NYJQSF: }0 ‘Wikipedia’ https://en.wikipedia.org/wiki/Order_of_operations except
 ^{NYJQNG:} ‘order’, especially ‘order of operation’ so referring to ‘procedures to perform first in order to evaluate’
 ^{NYJQPM:} is a common view as typically this is also the same but
 ^{NYJQPZ:} is wrong as gets into the still seperate issue of evaluation strategy
 ^{NYJQNG:} ‘order’, especially ‘order of operation’ so referring to ‘procedures to perform first in order to evaluate’
 ^{NYJPUC: }‘‘name’ ‘anew’’
 ^{NYJUD0:} ‘‘rendering’ ‘anew’’ ‘‘‘operation/phrase’ ‘default connections’’’
 ^{NYJPX5: }root: ‘operation/phrase’
 ^{NYJUCE: }‘default connections’
 ^{NYJPXP:} ‘default grouping’
 ^{NYJUKI:} ‘operator precidence’
 ^{NYJUPV:} problem from worst first:
 ^{NYJUSU:} topic generalized here (debatably) to cover other NYJUCE(‘default connections’) notably default operand values.
 ^{NYJURB:} if precidence is taken (as it it commonly) is beyond syntac grouping but to evalaution order, then #NYJULJ applies.
 ^{NYJUPV:} problem from worst first:
 ^{NYJUK2:} ‘order of operations’
 ^{NYJULJ:} killer problem #NYJQNG
 ‘for remainder, sections overall’
 ^{NYJRH3: } ‘usage’
 ^{NX1HOJ} ‘’ ‘‘operator’’
 ^{NX1IPK} ‘‘definition’ ‘anew’’
 ^{NYJE9Q:} per the operator
 ^{NYJNXW:} in some contexts, may be implied. Example:
 ^{NYJO3W:} ‘xy’ can mean ‘x*y’ where ‘*‘ is multiplication
 ^{NYJO53:} ‘red dog’ can mean ‘dog intersect red’
 ^{NYJOAF:} just another of the operand(s)
 ^{NYJOCX:} a possiblity
 ^{NYJODK:} which is rare but conceivable
 ^{NYJOF6:} makes computablity complex possibly impossible
 ^{NYJOIS:} natural notably long term proper
 ^{NYJOJQ:} probably not
 ^{NYJOCX:} a possiblity
 ^{NYJOYG:} for a clause ‘operation/phrase’, the verb –at least on quick look
 ^{NX1IPX} [replaced] (probably) a function specified by a standard symbol
 ^{NYJEAZ:} ‘replacement’ #NYJE9Q
 ‘notable pros thru cons:’
 ^{NX1HWV} ^{ }‘per def’ ‘same or similar’ ‘sub’
 ^{NX1HXB} <0
 ^{NX1HYJ} 0
 ^{NX1HZB} ‘Wikipedia’ ‘‘anew’’
 ^{NYISNA:} #NYIRSD
 ^{NX1I3L} #NYIQIL instances ‘operator’
 ^{NX1HZU} https://en.wikipedia.org/wiki/Operator_(computer_programming)
 ^{NX1I5I} https://en.wikipedia.org/wiki/Operator_(mathematics) except
 ^{NYJPOT:} as far as domains & codomains possible, appears incomplete
 ^{NYJPP5:} no mention of ‘symbol’
 ^{NYJPQ1:} no mention of ‘precidence’
 ^{NX1HZB} ‘Wikipedia’ ‘‘anew’’
 ^{NX1IMS} >0 common (including suggested much more confusingly from here)
 ^{NX1IM8} inequality { ≤, ≥} applied to real numbers
 ^{NX1IMK} but notably applicable not to complex numbers as that here has only a ‘reflexive partial order’}
 ^{NX1IM8} inequality { ≤, ≥} applied to real numbers
 ^{NX1HTT} ‘‘name’ ‘anew’’
 ^{NX1HUD} ‘operator’
 ^{NX1HV3} ‘‘rendering’ ‘anew’’ ‘‘operator’’
 ^{NX1HUD} ‘operator’
 ^{NYEYE3: }‘‘section history additional’ ‘in reverse start order’:’
 ^{NYIR65:} location: from /5129#NWWQ6B kid last to here
 ^{NYEYED: }location: from /5138#NWZ067 kid to here
 ^{NX1IPK} ‘‘definition’ ‘anew’’
 ^{NYJFHE:} ‘usage’
 ^{NYIPF4:} ‘’ ‘‘function’’
 ‘‘definition’ ‘anew’’
 ^{NYIPR9:} ^{ }‘per def’ ‘same or similar’ ‘sub’
 ^{NYIPFX:} ‘‘name’ ‘anew’’ ‘function’ ‘‘rendering’ ‘anew’’ ‘‘function’’
 ^{NYIPH6:} ‘‘‘Pretty Link’ entry’ ‘anew’’ section 1st
 ‘for remainder, sections overall’
 ^{NYIPWQ:} ‘’ ‘‘binary ‘function’’’
 ‘‘definition’ ‘anew’’
 ^{NYIPYK: }^{ }‘per def’ ‘same or similar’ ‘sub’
 <0
 ^{NYIPZ9: }0 ‘Wikipedia’ https://en.wikipedia.org/wiki/Binary_function
 ^{NYIPVJ: }‘‘name’ ‘anew’’ ‘binary ‘function’’ ‘‘rendering’ ‘anew’’ ‘‘binary ‘function’’’
 ‘for remainder, sections overall’
 ^{NX0B3C} ‘’ ‘‘weighted graph’’
 ^{NX0BMO} ‘notable pros thru cons:’
 ^{NX0BZJ} where every weight is
 ^{NX0C1N} 1 or 0
 ^{NX0C23} is potentially any ‘binary endorelation’
 ^{NX0C31} can be a number other than 1 or 0
 ^{NX0C6W} is used as the primary formal/structured means for optimizing travel and resource distribution
 ^{NX0C1N} 1 or 0
 ^{NX2PZ7} ‘per def’ ‘same or similar’ ‘sub’
 ^{NX2PZX} <0
 ^{NX2Q0A} ‘1’ weighted multigraph
 ^{NX2Q0W} 0
 ^{NX0DTV} ‘{binary aka 2input} function from V*V to Number’ (where V is any set, called the vertices)
 ^{NX2Q1V} in some cases also a realvalued function
 ^{NX2Y03} ‘Wikipedia’
 ^{NX2Y3A} https://en.wikipedia.org/wiki/Glossary_of_graph_theory#Weighted_graphs_and_networks
 ^{NX2Y3K} https://en.wikipedia.org/wiki/Graph_(mathematics)#Weighted_graph
 ^{NYIO9Q:} https://en.wikipedia.org/wiki/Graph_(abstract_data_type) including ‘Structures that associate values to the edges
 ^{NX0DTV} ‘{binary aka 2input} function from V*V to Number’ (where V is any set, called the vertices)
 ^{NX2QB3} <0 common ‘1’
 ^{NX2QBN} ‘binary endorelation’
 ^{NX2PZX} <0
 ^{NX0BAH} ‘‘name’ ‘anew’’
 ^{NX0BBK} ‘weighted graph’
 ^{NX0BQU} ‘‘rendering’ ‘anew’’
 ^{NX0BR1} ‘‘weighted graph’’
 ^{NX0BQU} ‘‘rendering’ ‘anew’’
 ^{NX0BKO} ‘weighted ‘binary endorelation’’
 ^{NX0CEL} ‘network’
 ^{NX0CFK} ^{ }‘notable pros thru cons:’
 ^{NX0CFX} 2nd most common term for this –pro
 ^{NX0CGD} many less formal meanings –notable con
 ^{NX0CFK} ^{ }‘notable pros thru cons:’
 ^{NX0BBK} ‘weighted graph’
 ‘for remainder, sections overall’
 ^{NYIO1V:} ‘’
 ^{NX0CIA} ‘’ ‘‘binary endorelation’’
 ^{NYINEE:} ‘‘definition’ ‘anew’’:
 ^{NYINEZ:} see Wikipedia entries except as noted.
 ^{NYFOVR} –with variables/preface ‘for all x and y in [‘binary endorelation’] X (it holds that)…’
 ^{NX0CO7} ‘notable pros thru cons:’
 ^{NX0CMR} seemingly the most common of its superclass
 ^{NX0BXJ} ‘per def’ ‘same or similar’ ‘sub’
 ^{NX0CPH} <0
 ^{NX0CQG} ‘1’ ‘weighted graph’
 ^{NX0JBC} 0
 ^{NX0JBN} ‘Wikipedia’ https://en.wikipedia.org/wiki/Binary_relation#Relations_over_a_set
 ^{NX0JDE} –an excellent reference.
 ^{NX0JBN} ‘Wikipedia’ https://en.wikipedia.org/wiki/Binary_relation#Relations_over_a_set
 ^{NX1RFZ} >0 common
 ^{NX1RGA} NX1RGA: ‘Wikipedia’ https://en.wikipedia.org/w/index.php?title=Binary_relation&oldid=684344533#Relations_over_a_set ‘Some important properties’
 ^{NYFKJD} by most salient/biggest features first:
 ^{NX1RNP} transitivity amount
 ^{NX1RW0} symmetry:
 ^{NYFOMB} 1: ‘1’ ‘’total: .. xRy or yRx (or both). This definition for total is different from left total in the previous section. For example, ≥ is a total relation.’
 ^{NYFP62} ‘per def’ ‘same or similar’ ‘sub’ <0 ‘reflexive’ per here
 ^{NX1RZJ} 1: ‘1’ ‘symmetric: ..if xRy then yRx. “Is a blood relative of” is a symmetric relation, because x is a blood relative of y if and only if y is a blood relative of x.’
 ^{NX1S2N} 0: ‘1’ ‘antisymmetric: ..if xRy and yRx then x = y. For example, ≥ is antisymmetric (so is >, but only because the condition in the definition is always false).^{[18]}’
 ^{NX1S2V} ‘same or similar’ ‘sub’ >0 common ‘1’ ‘asymmetric: ..if xRy then not yRx. A relation is asymmetric if and only if it is both antisymmetric and irreflexive.^{[19]} For example, > is asymmetric, but ≥ is not.’
 ^{NYFOMB} 1: ‘1’ ‘’total: .. xRy or yRx (or both). This definition for total is different from left total in the previous section. For example, ≥ is a total relation.’
 ^{NYHZ2Q} ‘binary endorelation’ reflexivity’
 ^{NX0CPH} <0
 ^{NX0DGE} ‘‘name’ ‘anew’’
 ^{NX0DGM} ‘binary endorelation’
 ^{NX0E4A} ‘‘rendering’ ‘anew’’
 ^{NYHSK0} ‘‘binary endorelation’’
 ^{NX0E4M} ‘‘binary endorelation’’
 ^{NX0E4A} ‘‘rendering’ ‘anew’’
 ^{NX0IKZ} ‘homogeneous binary relation’
 ^{NX0IUR} ‘simple directed graph permitting loops’
 ^{NX0IA8} ‘directable binaryweighted unigraph’
 ^{NX0ILN} where my additions of…
 ^{NX0IMB} ‘directable’ to insure it’s not undirected but not require it be directed.
 ^{NX0INI} ‘binaryweighted’ to make sure it’s not a general ‘weighted graph’
 ^{NX0IOO} ‘unigraph’ to make sure it’s not a multigraph
 ^{NX0ILN} where my additions of…
 ^{NX0DGM} ‘binary endorelation’
 ‘for remainder, sections overall’
 ^{NYGN07} ‘’ ‘‘‘binary endorelation’ P closure’’
 ^{NYGN42} ‘‘name’ ‘anew’’ ‘‘binary endorelation’ P closure’ ‘‘rendering’ ‘anew’’ ‘‘‘binary endorelation’ P closure’’
 ^{NYGN3P} ‘per def’ ‘same or similar’ ‘sub’
 ^{NYGN3B} 1 ‘1’ P
 ^{NYGN32} ‘Wikipedia’s P closure’: 0 ‘Wikipedia’ https://en.wikipedia.org/wiki/Closure_(mathematics)#P_closures_of_binary_relations
 ^{NYFKHL} common
 ‘for remainder, sections overall’
 ^{NX1S4P} ‘’ ‘‘‘binary endorelation’ reflexivity’’
 ^{NYHRTF} ‘‘definition’ ‘anew’’
 ^{NYHRPO} the reflexivity of a relation on given scale.
 ^{NYHRSC} degree/amount
 ^{NYHXW1} Yes: ‘1’ ‘reflexive ‘binary endorelation’’
 ^{NYHY8W} No: ‘1’
 ^{NX1S7M} ‘irreflexive (or strict): .. not xRx. For example, > is an irreflexive relation, but ≥ is not.’
 ^{ }‘per def’ ‘same or similar’ ‘sub’
 <0 {graded Yes/No measure of a property’s presence}
 0
 ‘Wikipedia’
 https://en.wikipedia.org/w/index.php?title=Transitivity&oldid=688335497#Logic_and_mathematics especially on ‘relation’
 NX1RGA reflexive
 ‘notable pros thru cons:’
 ‘Wikipedia’
 ^{NYHYRO} ‘‘name’ ‘anew’’ ‘‘binary endorelation’ reflexivity’ ‘‘rendering’ ‘anew’’ ‘‘‘binary endorelation’ reflexivity’’
 ‘for remainder, sections overall’
 ^{NX1S6T} ‘’ ‘‘reflexive ‘binary endorelation’’’
 ^{NYHXXM} ‘‘definition’ ‘anew’’
 ^{NYHXXA} ‘reflexive: .. xRx. For example, “greater than or equal to” (≥) is a reflexive relation but “greater than” (>) is not.’
 ^{NYHY1V} ‘per def’
 ^{NYHY1O} ‘notable pros thru cons:’
 ‘same or similar’ ‘sub’
 <0
 0
 ^{NX1QPY} >0 common
 ^{NYHSD4} ‘‘name’ ‘anew’’
 ^{NYHSDV} ‘reflexive ‘binary endorelation’’ ‘‘rendering’ ‘anew’’ ‘‘reflexive ‘binary endorelation’’’
 ^{NYHXXM} ‘‘definition’ ‘anew’’
 ^{NYHRTF} ‘‘definition’ ‘anew’’
 ^{NX1ZHK} ‘’ ‘‘relation transitivity’’
 ^{NX280M} ‘‘definition’ ‘anew’’
 ^{NX2813} the degree on this scale a relation has transitivity
 ^{NX1ZU8} degree/amount
 ^{NX1ZYW} Yes
 ^{NX1RO7} ‘1’ ‘‘transitive relation’’
 ^{NX1VBD} ‘per def’ ‘unique pros thru cons’
 ^{NX2003} for any 2 elements, to identify between them any {transitive connection, a powerful thing}, tests required are just 3 {aRb & aRb, plus {a=b} iff R is not reflexive} instead of up to the path length
 ^{NX1VBQ} per #NX28LS, with limited exception, representing & reasoning in general requires {computation or storage which are somewhat interchangeable} of size O(~n or n^2 or perhaps more)
 ^{NX2JWY} except for seemingly
 ^{NX2K08} partial equivalence thanks to good unionfind (aka disjointset) algorithms
 ^{NX2L0R} under the hood doing No but appearing Yes by internally bridging that gap via
 ^{NX2K9P} where a difference between any 2 pair can be generally computed in time proportionate to the size of the element ids as
 ^{NX2K6O} ‘total order’ over say numbers or strings in most cases
 ^{NX2KJB} bloom filter or equivalent on a {‘‘partial order’’ as pure transitive seems not enough there}
 ^{NX2KUQ} using memoization but could be a crapshoot
 ^{NX2K9P} where a difference between any 2 pair can be generally computed in time proportionate to the size of the element ids as
 ^{NX2JWY} except for seemingly
 ^{NX2N69} totally unknown to moderate No
 ^{NX2CBU} totally unknown
 ^{NX2N8A} minimal No
 ^{NX2NBQ} ‘1’ intransitive
 ^{NX09GH} ‘No for path length <=2’
 ^{NX2NFD} ‘1’ “antitransitive”
 ^{NX2NJ0} note the name ‘antitransitive’ is misleading as
 ^{NX2NLY} suggest it would completely undoes what transitive does but transitive makes connections of large path length but
 ^{NX2NO3} this definition only says ‘No for path length <=2’
 ^{NX09OC} as transitive cases recursively implied, notably {e(1)Re(2) & .. & e(n1)Re(n) and e(1)Re(n)} for n>3, this antitrans def misses
 ^{NX2NJ0} note the name ‘antitransitive’ is misleading as
 ^{NX2NFD} ‘1’ “antitransitive”
 ^{NX2N7Z} ‘per def’ ‘unique pros thru cons’
 ^{NX2CC5} low indeed lowest computation costs
 ^{NX2JHE} bad {consistency & duplicate detection} for where transitivity is intended (normal) but here being informally maintained
 ^{NX2CFN} No
 ^{NX2KWS} ^{ }‘per def’ ‘unique pros thru cons’
 ^{NX2JH2} low indeed lowest costs for storage so also duplicate detection & updates
 ^{NX2P67} ‘can also be found in time O(nm)’*
 ^{NX1RQ0} ‘1’
 ^{NX090F} ‘’ ‘‘transitive reduction’’
 ^{NX09XQ} ‘‘definition’ ‘anew’’: given in its name.
 ^{NX0A3R} ‘notable pros thru cons:’
 ^{NX0A42} key if not essential as a canonical form for most {{compactly representing} + {effectively reasoning about (example: for distance)}} any partial order, by both humans & computers
 ^{NX0A9J} this point I have never seen mentioned anywhere
 ^{NX0ABS} which surprises me & I can’t explain it.
 ^{NX0A9J} this point I have never seen mentioned anywhere
 ^{NX0A42} key if not essential as a canonical form for most {{compactly representing} + {effectively reasoning about (example: for distance)}} any partial order, by both humans & computers
 ^{NX0AD2} usage
 ^{NX0AGQ} as a product of some specification
 ^{NX0ADV} –as its name core ‘reduction’ suggests
 ^{NX0APY} ideally with warnings where the specification {overspecified or (if cycles aren’t allowed) introduced a cycle}
 ^{NX0AIM} a good idea
 ^{NX0AJJ} ironically I’ve never seen this usage
 ^{NX0AKE} specified directly
 ^{NX0AM8} such as specifying a factor of primes
 ^{NX0AL9} so with the assumption/hope that it matches what should be
 ^{NX0AOB} often without any validation of that
 ^{NX0ATE} is the usage I’ve so far always seen
 ^{NX0AGQ} as a product of some specification
 ^{NWXRAS} ^{ }‘per def’
 ^{NX2OB3} ‘same or similar’ ‘sub’
 ^{NWXRE0} <0 ‘1’ “antitransitive”
 ^{NWXQDU} <=0 its source
 ^{NX2OL0} 0
 ^{NX2OCH} ‘Wikipedia’ https://en.wikipedia.org/wiki/Transitive_reduction including
 ^{NX2P2D} ‘can also be found in time O(nm), a bound that may be faster than the matrix multiplication methods for sparse graphs’ which are typical.
 ^{NX2OCH} ‘Wikipedia’ https://en.wikipedia.org/wiki/Transitive_reduction including
 ^{NX2OLK} >0 common {same as for transitive}
 ^{NX2OB3} ‘same or similar’ ‘sub’
 ^{NX095B} ‘‘name’ ‘anew’’
 ^{NX095N} ‘transitive reduction’
 ^{NX09UY} ‘‘rendering’ ‘anew’’
 ^{NX09VJ} ‘‘transitive reduction’’
 ^{NX09UY} ‘‘rendering’ ‘anew’’
 ^{NX095N} ‘transitive reduction’
 ^{NX090F} ‘’ ‘‘transitive reduction’’
 ^{NX2KWS} ^{ }‘per def’ ‘unique pros thru cons’
 ^{NX1ZYW} Yes
 ^{NX1ZRX} ^{ }‘per def’ ‘same or similar’ ‘sub’
 ^{NX2PHU} <0 {graded Yes/No measure of a property’s presence}
 ^{NX1ZSK} 0
 ^{NX1ZT7} ‘Wikipedia’
 ^{NX2LII} https://en.wikipedia.org/w/index.php?title=Transitivity&oldid=688335497#Logic_and_mathematics especially on ‘relation’
 ^{NX1ZTN} NX1RGA transitive
 ‘notable pros thru cons:’
 ^{NX1ZT7} ‘Wikipedia’
 ^{NX1ZNX} ‘‘name’ ‘anew’’ ‘relation transitivity’
 ^{NX1ZP8} ^{ }‘‘rendering’ ‘anew’’ ‘‘relation transitivity’’
 ‘for remainder, sections overall’
 ^{NX1PXP} ‘’ ‘‘transitive relation’’
 ^{NX1QKS} ‘‘definition’ ‘anew’’
 ^{NX1V7W} transitive (relation type)
 ^{NX1PZF} ‘notable pros thru cons:’
 ^{NX1PZ7} seemingly the most formally familiar of its main superclass
 ^{NX28D7} ^{ }‘per def’
 ^{NX28DK} for any 2 elements e(1) & e(n),
 ^{NX28FO} e(1)Re(n) implies between the two elements there exists a path (of existing intermediate elements), specifically a transitive connection e(1)Re(2) & .. & e(n1)Re(n),
 ^{NX28LJ} going only in the direction given: starting at a and ending at b
 ^{NX28LS} which can be as long (as many jumps) as the max of {{the total number of elements minus 1}, 0}
 ^{NX28FO} e(1)Re(n) implies between the two elements there exists a path (of existing intermediate elements), specifically a transitive connection e(1)Re(2) & .. & e(n1)Re(n),
 ^{NX1Q1P} ‘same or similar’ ‘sub’
 ^{NX1Q28} <0
 ^{NX0K6S} ‘1’ ‘binary endorelation’ notably transitive (relation type)
 ^{NX1QML} 0
 ^{NX1QPY} >0 common
 ^{NX1QVQ} reflexivity
 ^{NX1QVG} 1: ‘1’ ‘‘preorder’’
 ^{NX1QRQ} symmetry
 ^{NX1QYE} 1: ‘1’ partial equivalence
 ^{NX1R23} 0: ‘1’ ‘‘partial order’’
 ^{NX1QVQ} reflexivity
 ^{NX1Q28} <0
 ^{NX28DK} for any 2 elements e(1) & e(n),
 ^{NX1PV1} ‘‘name’ ‘anew’’
 ^{NX1PVF} ‘transitive relation’
 ^{NX1PWS} ‘‘rendering’ ‘anew’’ ‘‘transitive relation’’
 ^{NX1PVF} ‘transitive relation’
 ‘for remainder, sections overall’
 ^{NYGKUH} ‘’ ‘‘transitive closure’’
 ^{NYGKV0} ‘‘name’ ‘anew’’ ‘transitive closure’ ‘‘rendering’ ‘anew’’ ‘‘transitive closure’’
 ^{NYGLOF} ‘per def’ ‘same or similar’ ‘sub’
 ^{NYGLFY} 1 ‘1’ ‘‘transitive relation’’
 ^{NYGLN8} 0
 ‘for remainder, sections overall’
 ^{NYFPSS} transitive (relation type) and {reflexive (relation type) or/and antisymmetric (relation type)}
 ‘for remainder, sections overall’
 ^{NX0K04} ‘’ ‘‘preorder’’
 ^{NX1PES} ‘‘definition’ ‘anew’’
 ^{NX1PFS} transitive
 ^{NX1SRP} reflexive (relation type)
 ^{NX5896} ‘per def’
 ^{NX0KII} ‘notable pros thru cons:’
 ^{NX0KG9} seemingly the most common of its superclass
 ^{NX0K4X} ‘same or similar’ ‘sub’
 ^{NX0K5D} <0
 see def
 ^{NX0K73} 0
 ^{NX0K5D} <0
 ^{NX0KII} ‘notable pros thru cons:’
 ^{NX0K9P} ‘‘name’ ‘anew’’
 ^{NX0KAD} ‘preorder’
 ^{NX0KBW} ‘‘rendering’ ‘anew’’
 ^{NX0KC5} ‘‘preorder’’
 ^{NX0KBW} ‘‘rendering’ ‘anew’’
 ^{NX0KAD} ‘preorder’
 ‘for remainder, sections overall’
 ^{NYGM5F} ‘’ ‘‘equivalence relation’’
 ^{NYGM88} ‘‘name’ ‘anew’’ ‘equivalence relation’ ‘‘rendering’ ‘anew’’ ‘‘equivalence relation’’
 ^{NYGMCN} ‘per def’ ‘same or similar’ ‘sub’
 ^{NYGM6X} 1 ‘1’ ‘‘preorder’’
 ^{NYGM6C} 0 ‘Wikipedia’ https://en.wikipedia.org/wiki/Equivalence_relation#Definition
 ‘for remainder, sections overall’
 ^{NYGMF6} ‘’ ‘‘congruence relation’’
 ^{NYGMMH} ‘‘name’ ‘anew’’ ‘congruence relation’ ‘‘rendering’ ‘anew’’ ‘‘congruence relation’’
 ^{NYGMP8} ‘per def’ ‘same or similar’ ‘sub’
 ^{NYGMKG} 1 ‘1’ ‘‘equivalence relation’’
 ^{NYGMJR} 0 ‘Wikipedia’ https://en.wikipedia.org/wiki/Congruence_relation
 ^{NYHG8R} 1 common ‘1’ with the property that
 ‘for remainder, sections overall’
 ^{NX5H3R} ‘’ ‘‘congruence closure’’
 ^{NX5H46} ‘‘definition’ ‘anew’’
 ^{NX5H65} ‘per def’ ‘same or similar’ ‘sub’
 ^{NYGLU3} 1 ‘1’ ‘‘transitive closure’’
 ^{NYGLX1} 0
 ^{NX5H4H} https://www.google.com/search?q=congruence+closure
 ^{NYHFHB} ‘Wikipedia’
 ^{NYHFHQ} in ‘Wikipedia’s P closure’.
 ^{NYHFO3} found no other.
 ‘maker’
 ^{NX5H6I} ‘notable pros thru cons:’
 ^{NX5H6Q} seemingly essential for reliably finding normal/canonical form
 ^{NX5HEO} ‘same or similar’ ‘sub’
 ^{NX5HEZ} <0 {closure}
 ^{NX5H8R} ‘‘name’ ‘anew’’ ‘congruence closure’
 ^{NX5HGT} ‘‘rendering’ ‘anew’’ ‘‘congruence closure’’
 ^{NX5H9E} ‘‘‘Pretty Link’ entry’ ‘anew’’ 1st
 ^{NX1PES} ‘‘definition’ ‘anew’’
 ^{NX1O6W} ‘’ ‘‘partial order’’
 ^{NX1P3P} ‘‘definition’ ‘anew’’
 ^{NX1R7K} ‘‘transitive relation’’
 ^{NX1P47} antisymmetric (relation type)
 ^{NX1OAS} ‘per def’ ‘same or similar’ ‘sub’
 ^{NX1OB8} <0
 ^{NX1PLX} see def
 ^{NX1OOC} 0
 ^{NX1O7D} ‘notable pros thru cons:’
 ^{NX1O7T} seemingly the most formally familiar of its main superclass
 ^{NX1OP0} ‘Wikipedia’ https://en.wikipedia.org/w/index.php?title=Partially_ordered_set&oldid=687708579#Strict_and_nonstrict_partial_orders
 ^{NX1O7D} ‘notable pros thru cons:’
 ^{NX1OQZ} >0 common
 ^{NX1OZ6} strict/reflexive or not
 ^{NX0UU7} consequences including consequential theorems
 ^{NX0UGI} for every partial order, the only difference between nonstrict vs. strict is reflexive vs. irreflexive
 ^{NX0UIH} per the combo:
 ^{NX0UNN} ‘A (nonstrict[ (or reflexive, or weak)*] ) partial order^{[2]} is a binary relation “≤” over a set P which is reflexive, antisymmetric, and transitive’ says here
 ^{NX0UJ4} ‘ a strict (or irreflexive) partial order “<” is a binary relation that is irreflexive, transitive and asymmetric’ says here
 ^{NX0UTX} ‘A relation is asymmetric if and only if it is both antisymmetric and irreflexive.^{[2]}’ says here & #NX1S2V
 ^{NX0UIH} per the combo:
 ^{NX0UGI} for every partial order, the only difference between nonstrict vs. strict is reflexive vs. irreflexive
 ^{NX1OSM} ‘1’ ‘‘reflexive partial order’’
 ^{NX0UU7} consequences including consequential theorems
 ^{NX1OZ6} strict/reflexive or not
 ^{NX1OB8} <0
 ^{NX1O8D} ‘‘name’ ‘anew’’
 ^{NX1O8T} ‘partial order’
 ^{NX1OJ9} ‘‘rendering’ ‘anew’’ ‘‘partial order’’
 ^{NX1O8T} ‘partial order’
 ^{NX1P3P} ‘‘definition’ ‘anew’’
 ^{NX0S1F} ‘’ ‘‘reflexive partial order’’
 ^{NX1SWK} ‘‘definition’ ‘anew’’
 ^{NX1T91} ‘‘transitive relation’’
 ^{NX1T9V} antisymmetric (relation type)
 ^{NX1TAF} reflexive (relation type)
 ^{NX0U3H} ‘notable pros thru cons:’
 ^{NX0T1E} seemingly the most common of its superclass
 ^{NX0BP4} commonplace tools to represent & reasonwith them are still weak
 ^{NX0SH5} ‘per def’ ‘same or similar’ ‘sub’
 ^{NX0T24} <0
 ^{NX0T3U} 0
 ^{NX1OMW} ‘‘partial order’’ AND reflexive (relation type)
 ^{NX0T2S} ‘‘preorder’’ AND antisymmetric (relation type)
 ^{NX0T4F} ‘Wikipedia’ https://en.wikipedia.org/wiki/Partially_ordered_set#Formal_definition
 ^{NWYSR5} >0 common (including suggested in here)
 ^{NWYSVF} ‘isa’ including social parenting & subset
 ^{NWYT4N} hasa
 ^{NWYSZT} ‘instanceof’ probably especially when there are relation chains as in prototypebased programming
 ^{NX0S4P} ‘‘name’ ‘anew’’
 ^{NX0S53} ‘reflexive partial order’
 ^{NX0S7J} ‘‘rendering’ ‘anew’’ ‘‘reflexive partial order’’
 ^{NX0U18} ‘nonstrict partial order’
 ^{NX0U4O} usage: per #NX0UGI, prefer instead variant ‘reflexive’/‘irreflexive’ as that fully specifies the difference (instead of having to know strict for this context)
 ^{NX0S53} ‘reflexive partial order’
 ‘for remainder, sections overall’
 ^{NX1GI7} ‘’ ‘‘total order’’
 ^{NX1GVA} ‘notable pros thru cons:’
 ^{NX1GVM} seemingly the most formally familiar of its main superclass
 ^{NX1GVX} commonplace tools to reasonwith them are very strong
 ^{NX1GXW} ‘same or similar’ ‘sub’
 ^{NX1GYX} <0
 ^{NX1GZD} ‘1’ ‘‘reflexive partial order’’
 ^{NX1H3U} 0
 ^{NYFPEU} ‘1’ { total (relation type) and ‘partial order’ }
 ^{NX1H48} ‘Wikipedia’ https://en.wikipedia.org/wiki/Total_order
 ^{NX1H59} >0 common (including suggested much more confusingly from here)
 ^{NX1H90} inequality { ≤, ≥} applied to real numbers
 ^{NX1HJP} but notably applicable not to complex numbers as that here has only a ‘reflexive partial order’}
 ^{NX1H90} inequality { ≤, ≥} applied to real numbers
 ^{NX1GYX} <0
 ^{NX1GPI} ‘‘name’ ‘anew’’
 ^{NX1GQB} ‘total order’
 ^{NX1GRC} ‘‘rendering’ ‘anew’’ ‘‘total order’’
 ^{NX1GQB} ‘total order’
 ^{NX1GVA} ‘notable pros thru cons:’
 ^{NX1SWK} ‘‘definition’ ‘anew’’
 ^{NX1QKS} ‘‘definition’ ‘anew’’
 ^{NX280M} ‘‘definition’ ‘anew’’
 s
 ^{NYHGMI} ‘’ ‘‘congruence property type’’
 ^{NYHHPQ} ‘‘definition’ ‘anew’’
 ^{NYHI46} property(s) which (seemingly equivalently):
 ^{NYHHQ2} when combined with ‘equivalence relation’ assertion, create a ‘congruence relation’
 ^{NYHI2L} turn a given ‘equivalence relation’ into a ‘congruence relation’
 ^{NYHI46} property(s) which (seemingly equivalently):
 ^{NYHKDW} ‘‘motivation or source or change’ ‘in reverse start order’’
 ^{NYHIJM} ‘‘name’ ‘anew’
 ^{NYHIN9} ‘congruence property type’
 ^{NYHIP1} ‘‘rendering’ ‘anew’’ ‘‘congruence property type’’
 ^{NYHGNV} ‘congruence property’
 ^{NYHIN9} ‘congruence property type’
 ^{NYHIAE} ‘per def’ ‘same or similar’ ‘sub’
 1 ‘1’
 ^{NYHI78} 0
 my finds
 ^{ }
 my finds
 ‘for remainder, sections overall’
 ^{NYHJA3} ‘’
 ^{NYHJ6T} ‘‘definition’ ‘anew’’
 ^{NYHKXA} a binary endorelation R where, given S1 & S2 which are each a array or equivalent, {S1 R S2} if
 ^{NYHIUW} for every i, {S1[i] R S2[i]}
 ^{NYHLQD} Note when condition
 ^{NYHMDA} of both
 ^{NYHMDM} {R is not reflexive}
 ^{NYHMFU} which seems possible
 ^{NYHMEV} {i has only 1 value}
 ^{NYHLR7} which is extremely rare (as the structure would contain little content except say for say nested quoteprotection)
 ^{NYHMDM} {R is not reflexive}
 ^{NYHLRF} #NYHIUW does not seem to do much useful, a problem with #NYHIUW possibly; how to fix? Possibilities:
 ^{NYHMDA} of both
 ^{NYHLQD} Note when condition
 ^{NYHPUB} {for every i, {S1[i] R S2[i]} or {S1[i] = S2[i]}} and {for some i, {S1[i] R S2[i]}}
 ^{NYHMMY} where ‘or {S1[i] = S2[i]}’
 ^{NYHQCZ} is to help solve #NYHMDM
 ^{NYHMOI} as for ‘a sum S1 is lessthan a sum S2 if respective augments pairwise are less than OR sane as’
 ^{NYHQI0} problem is the ‘=’ operator here is readily stricter than a congruence intended by R
 ^{NYHQCZ} is to help solve #NYHMDM
 ^{NYHMMY} where ‘or {S1[i] = S2[i]}’
 ^{NYHIUW} for every i, {S1[i] R S2[i]}
 ^{NYHJB8} ‘array or equivalent’ includes:
 ^{NYHJD4} very commonly an application A of a function to its arguments, where say A[i] is the respective argument except that A[0] is the function.
 ^{NYHKXA} a binary endorelation R where, given S1 & S2 which are each a array or equivalent, {S1 R S2} if
 ^{NYHHF7} ‘‘motivation or source or change’ ‘in reverse start order’’
 ^{NYHHGG} since I couldn’t find a formal term that defines this, my invention.
 ^{NYHHFH} ~10 min ago, seeing https://www.google.com/search?q=congruence+closure find 1 (http://www.cs.berkeley.edu/~necula/autded/lecture12congclos.pdf) slide 2 (‘Theory of Equality’) list the 3 properties of equivalence relation plus 1 additional labeled ‘congruence’
 ^{NYHHNP} In bachelors thesis (on memoized evaluation) else masters thesis, I probably defined something similar.
 ‘‘name’ ‘anew’
 ^{NYHIN9} ‘substitutive ’
 ^{NYHKQC} ‘substitutive’ from #NYHJMU
 ‘‘rendering’ ‘anew’’ ‘‘congruence property type’’
 ^{ }
 ^{NYHIN9} ‘substitutive ’
 ‘per def’
 ^{NYHJJS} ‘same or similar’ ‘sub’
 ^{NYHJ80} <0 ‘1’ ‘‘congruence property type’’
 ^{NYHI78} 0
 ^{NYHI91} my finds
 ^{NYHI7L} ‘Wikipedia’ find not.
 ^{NYHI80} Google Searching: find not
 ^{NYHI91} my finds
 ^{NYHJO7} >0 common
 ^{NYHJMU} When R is a full ‘congruence relation’, {much of https://en.wikipedia.org/wiki/Substitution#Science_and_mathematics} for an equivalent.
 ^{NYHJJS} ‘same or similar’ ‘sub’
 ^{NYHJ6T} ‘‘definition’ ‘anew’’
 ^{NYHHPQ} ‘‘definition’ ‘anew’’
 ^{NYINEE:} ‘‘definition’ ‘anew’’:
 ^{NYIQHC:} ‘’ ‘‘operation/phrase’’
 annex
 ‘motivation’
 ‘success of this’
 ^{NWZ077} ‘post history additional’: ‘‘post history additional’ ‘in reverse start order’:’
 ^{NYHZUI} ‘{post.status.snapshot{;date ’20151127Fri1557pst‘;after ID ’minutes 0‘;revision ’11‘;version ’4.0‘;words ’5661‘;as ’before finished with split just got Chrome ‘Aw, Snap!’ so on reload got ‘There is an autosave of this post that is more recent than the version below. View the autosave’ giving updates {move out #NOKXS2 thru #NX7H28 + diffs #NX090F thru #NX1OJ9 (diff sync failed) + move out #NX1HOJ thru #NX5H9E with diffs & ending at #NX5JL3 + history #NYENE9 thru #NYEMSB} + ‘Post restored to revision from November 27, 2015 @ 23:40:24 [Autosave]’ + ‘The backup of this post in your browser is different from the version below. Restore the backup.’ which included {~15 characters more after #NYHZ2Q} & looked current on good look‘;do ’continue editing starting with #NXS2YK with
694 replacements‘}}’  ^{NYENE9} split of this post
 ^{NYENF8} into subposts
 ^{NYENND} graphs overall –this article
 ^{NYEZ4O} compare & review
 ^{NYENFS} ‘motivation & review’
 ^{NYENG2} ‘displacement/offset & categorizing’
 ^{NYENHX} ‘Pretty Link’ stuff moves to name & ref –done into /5160#NYEO3T
 ^{ }
 ^{NYENF8} into subposts
 ^{NYEMSB} ‘{post.status.snapshot{;date ’20151125Wed2022pst‘;after ID ’minutes 0‘;revision ’10‘;version ’3.1‘;words ’8852‘;as ’just got Chrome ‘Aw, Snap!’ so on refresh got ‘There is an autosave of this post that is more recent than the version below. View the autosave’ giving updates {#NYDNSD thru #NYDWWS + history #NYDRAJ: very few updates for another crash} + ‘Post restored to revision from November 25, 2015 @ 21:35:27 [Autosave]’ + ‘The backup of this post in your browser is different from the version below. Restore the backup.’ + ‘Post restored successfully. Undo.’ which gets the latest few characters ‘–also in spacetime so not’‘;do ’continue editing starting with #NXS2YK with
1107 replacements; eeks as we got only 800 words out of the last edit before another crash‘}}’  ^{NYDRAJ} ‘{post.status.snapshot{;date ’20151119Thu0945pst‘;after ID ’minutes 0‘;revision ’9‘;version ’3.0‘;words ’8062‘;as ’just got Chrome ‘Aw, Snap!’ so on reload got ‘There is an autosave of this post that is more recent than the version below. View the autosave’ giving updates {#NX5K6W moved + #NYCZD5 thru #NYCF3J + #NYD0IU thru #NYCVBG + #NYCTBF thru #NYCARG + history #NYCEZ9} + ‘Post restored to revision from November 25, 2015 @ 16:36:11 [Autosave]’ which looked very current on good look‘;do ’continue editing starting with #NXS2YK with
1056 replacements‘}}’  ^{NYCEZ9} ‘{post.status.snapshot{;date ’20151124Tue1539pst‘;after ID ’minutes 0‘;revision ’8‘;version ’2.0‘;words ’6770‘;as ’as editing crashed from either Chrome or OS bug, on reload got: ‘There is an autosave of this post that is more recent than the version below. View the autosave’ with {updates title + #NV8LHT + #NXKHDI thru #NX2XMJ + #NOW3JL thru #NOW3RB (a move) + #NXKCP5 thru #NXKCSN + history #NXKBWQ thru #NXKBVP} + ‘Post restored to revision from November 9, 2015 @ 21:44:44 [Autosave]’ ‘;do ’per NY0WO6 with _ replacements then continue editing‘}}’
 ^{NXKBWQ} updates: move #NOM5R5 + #NXKC3N + thru #NXKCSN + #NXKHDI + NX91CQ
 ^{NXKBVP} ‘{post.status.snapshot{;date ’20151109Mon1138pst‘;after ID ’minutes 0‘;revision ’7‘;version ’1.0‘;words ’6597‘;as ’Due to OS forced restart NXGEHV, didn’t properly save so on reload got ‘There is an autosave of this post that is more recent than the version below. View the autosave’ giving updates {#NX7HMB + #NX7HAP thru #NX7H28 + #NOM6YI thru #NVWNYD + #NWWOPP thru #NWWP51 + #NX75OM thru #NX75QA + #NX5JUV thru #NX5LMA} getting ‘Post restored to revision from November 3, 2015 @ 07:03:47 [Autosave]’ which has recency {unknown on quick look as no recent memory but probably ok}‘;do ’continue editing‘}}’
 ^{NX75JF} updates: many + {move ‘‘in comparison to’’ from /5129 to here /5138}
 ^{NX6CID} ‘{post.status.snapshot: date ’20151101Sun2225pst‘;after ID’ minutes 0‘;revision ’6‘;version ’0.6‘;words ’6102‘;as ’got ‘Aw, Snap!’ so reload getting There is an autosave of this post that is more recent than the version below. View the autosave’ has notable {{#NX5E7A thru #NX5GQS}+{#NX5E82 thru #NX5M7Z}} so do getting ‘Post restored to revision from November 2, 2015 @ 06:17:42 [Autosave]’ and no more but looks current including recent #NX6C4P ‘;do ’continue editing‘}’.
 ^{NX5BUS} ‘{post.status.snapshot: date ’20151101Sun1813pst‘;after ID’ minutes 0‘;revision ’5‘;version ’0.5‘;words ’5208‘;as ’got ‘Aw, Snap!’ so reload getting ‘There is an autosave of this post that is more recent than the version below. View the autosave’ has significant diffs including {#NX2XMJ thru #NWZ0W6}+{#NOKXS2 thru #NX4MTW}+{#NWW5RR thru #NWWE2R}+{#NX4GW3 thru #NWYEKT}+{#NWXYW2 thru ~#NX4EZK}+{#NWY6L8 thru ~#NX05EW}+{#NWXRAS thru #NX2OLK}+{#NX2PZ7 thru #NX0BBK}+{#NX28D7 thru #NX0K6S}+{#NX1ZHK thru #NX22LL}, select getting ‘Post restored to revision from November 1, 2015 @ 16:21:43 [Autosave]’ and ‘The backup of this post in your browser is different from the version below. Restore the backup.’ doing restores to last point adding #NX59H3‘;do ’continue editing‘}’.
 ^{NX3JE4} split out #NX3I60
 ^{NX22SY} continue latest entries,
 ^{NX22RH} ‘{post.status.snapshot: date ’20151030Fri1604pst‘;after ID’ minutes 0‘;revision ’4‘;version ’0.4‘;words ’4183‘;as ’got ‘Aw, Snap!’ so reload then ‘There is an autosave of this post that is more recent than the version below. View the autosave’ primarily showing {add #NX090F thru #NX1ZP8} do restore getting ‘Post restored to revision from October 30, 2015 @ 22:06:14 [Autosave]’ and ‘The backup of this post in your browser is different from the version below. Restore the backup.’ which gives a few changes bringing to latest ending in ~‘aRb or aRb’‘;do ’continue editing‘}’.
 ^{NX22LL} continue latest entries, mostly noted next
 ^{NX02PZ} ‘{post.status.snapshot: date ’20151029Thu1408pst‘;after ID’ minutes 0‘;revision ’1‘;version ’0.1‘;words ’2423‘;as ’significant todo but good to get content moved to here republished‘;do ’Publish 1 then continue editing‘}’.
 ^{NX0257} {spellcheck} + {update IDs to latest format: 312 replacements}
 ^{NX01TC} TODO: finish completing latest entries + proofread + verify links then {spellcheck} + {update IDs to latest format: __ replacements}
 ^{NWZMLP} for the content moved to here, do NWZNOM: { http://1.jothere.com/wpadmin/admin.php?page=prettylink&search=5129&size=100 ends up with 12 entries; http://1.jothere.com/wpadmin/admin.php?page=prettylink&search=5138&size=100 goes from 0 to 8 }
 ^{NWYUPJ} ‘{post.status.snapshot: date ’20151028Wed2217pst‘;after ID’ minutes 0‘;revision ’1‘;version ’0.1‘;words ’2548~‘;as ’to do /5129#NWYU94‘;do ’{at time of ID of this entry, so now}, do /5058#NW3WBQ where to get a reasonable template AND source text, from http://1.jothere.com/wpadmin/edit.php?post_type=post pick the post with the highest post #, well, since near enough, pick the source post, so post with last addition which is the last history entry /5129#NWYU94, creating this post http://1.JotHere.com/5138#NWYUYU then cut {all its content not to be reused here. so including every KCGUID declaration} to, after this, be completed”‘}’.
 ^{NYHZUI} ‘{post.status.snapshot{;date ’20151127Fri1557pst‘;after ID ’minutes 0‘;revision ’11‘;version ’4.0‘;words ’5661‘;as ’before finished with split just got Chrome ‘Aw, Snap!’ so on reload got ‘There is an autosave of this post that is more recent than the version below. View the autosave’ giving updates {move out #NOKXS2 thru #NX7H28 + diffs #NX090F thru #NX1OJ9 (diff sync failed) + move out #NX1HOJ thru #NX5H9E with diffs & ending at #NX5JL3 + history #NYENE9 thru #NYEMSB} + ‘Post restored to revision from November 27, 2015 @ 23:40:24 [Autosave]’ + ‘The backup of this post in your browser is different from the version below. Restore the backup.’ which included {~15 characters more after #NYHZ2Q} & looked current on good look‘;do ’continue editing starting with #NXS2YK with