Oct 292015
(definition LG5DEF) of (definition LG5DEF) LG5QVP, ‘this site's documentation for its users’, definition LG5DEF Add comments
- 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.
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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)
- 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
- 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
- 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 catch-22.
- 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 nicely-broken 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
- 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)
- NYJRMD: I recommend
- NYJROF: with the minimal exception of
- NYJS1F: {method call/member-access} is left-associative
- 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/member-access} is left-associative
- NYJSAB: as, from biggest reasons:
- NYJSEZ: clarity should always be preferred whenever practical (which it is), including
- 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 built-in operators with no change in their precidence (so same parser works)
- 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/can-the-ideal-language-allows-custom-operators/
- NYJV4L: significantly enabling helpful syntactic tools, as example
- 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:
- NYJOAF: just another of the operand(s)
- 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
- 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’
- 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’’’
- NX0B3C ‘-’ ‘‘weighted graph’’
- NX0BMO ‘notable pros thru cons:’
- NX0BZJ where every weight is
- NX2PZ7 ‘per def’ ‘same or similar’ ‘sub’
- NX2PZX <0
- NX2Q0W 0
- NX0DTV ‘{binary aka 2-input} function from V*V to Number’ (where V is any set, called the vertices)
- NX2Q1V in some cases also a real-valued 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 2-input} function from V*V to Number’ (where V is any set, called the vertices)
- NX2QB3 <0 common ‘1’
- NX0BAH ‘‘name’ ‘anew’’
- ‘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
- 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.’
- 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 anti-symmetric (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 anti-symmetric and irreflexive.[19] For example, > is asymmetric, but ≥ is not.’
- NYHZ2Q ‘binary endorelation’ reflexivity’
- NX0DGE ‘‘name’ ‘anew’’
- NX0DGM ‘binary endorelation’
- NX0IKZ ‘homogeneous binary relation’
- NX0IUR ‘simple directed graph permitting loops’
- NX0IA8 ‘directable binary-weighted uni-graph’
- NX0ILN where my additions of…
- NX0IMB ‘directable’ to insure it’s not undirected but not require it be directed.
- NX0INI ‘binary-weighted’ to make sure it’s not a general ‘weighted graph’
- NX0IOO ‘uni-graph’ to make sure it’s not a multigraph
- NX0ILN where my additions of…
- ‘for remainder, sections overall’
- NYGN07 ‘-’ ‘‘‘binary endorelation’ P closure’’
- 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
- ‘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’’’
- 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 union-find (aka disjoint-set) 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 crap-shoot
- 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
- NX09GH ‘No for path length <=2’
- NX2NFD ‘1’ “antitransitive”
- NX2NJ0 note the name ‘anti-transitive’ 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(n-1)Re(n) and e(1)Re(n)} for n>3, this anti-trans def misses
- NX2NJ0 note the name ‘anti-transitive’ is misleading as
- NX2NFD ‘1’ “antitransitive”
- NX2N7Z ‘per def’ ‘unique pros thru cons’
- NX2CFN No
- NX2KWS ‘per def’ ‘unique pros thru cons’
- 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
- NX0AD2 usage
- 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’’
- NX090F ‘-’ ‘‘transitive reduction’’
- 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’
- ‘for remainder, sections overall’
- NX1PXP ‘-’ ‘‘transitive relation’’
- NX1QKS ‘‘definition’ ‘anew’’
- 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(n-1)Re(n),
- NX1Q1P ‘same or similar’ ‘sub’
- NX1Q28 <0
- 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
- NX28DK for any 2 elements e(1) & e(n),
- NX1PV1 ‘‘name’ ‘anew’’
- NX1PVF ‘transitive relation’
- ‘for remainder, sections overall’
- NYGKUH ‘-’ ‘‘transitive closure’’
- NYFPSS transitive (relation type) and {reflexive (relation type) or/and antisymmetric (relation type)}
- ‘for remainder, sections overall’
- NX0K04 ‘-’ ‘‘preorder’’
- NX1PES ‘‘definition’ ‘anew’’
- NX5896 ‘per def’
- NX0KII ‘notable pros thru cons:’
- NX0KG9 seemingly the most common of its superclass
- NX0K4X ‘same or similar’ ‘sub’
- NX0KII ‘notable pros thru cons:’
- NX0K9P ‘‘name’ ‘anew’’
- ‘for remainder, sections overall’
- NYGM5F ‘-’ ‘‘equivalence relation’’
- NYGM88 ‘‘name’ ‘anew’’ ‘equivalence relation’ ‘‘rendering’ ‘anew’’ ‘‘equivalence relation’’
- NYGMCN ‘per def’ ‘same or similar’ ‘sub’
- ‘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
- 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’
- NX5H9E ‘‘‘Pretty Link’ entry’ ‘anew’’ 1st
- NX1O6W ‘-’ ‘‘partial order’’
- NX1P3P ‘‘definition’ ‘anew’’
- NX1OAS ‘per def’ ‘same or similar’ ‘sub’
- NX1OB8 <0
- 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_non-strict_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 non-strict vs. strict is reflexive vs. irreflexive
- NX0UIH per the combo:
- NX0UNN ‘A (non-strict[ (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 non-strict vs. strict is reflexive vs. irreflexive
- NX1OSM ‘1’ ‘‘reflexive partial order’’
- NX0UU7 consequences including consequential theorems
- NX1OZ6 strict/reflexive or not
- NX1O8D ‘‘name’ ‘anew’’
- NX1O8T ‘partial order’
- NX0S1F ‘-’ ‘‘reflexive partial order’’
- NX1SWK ‘‘definition’ ‘anew’’
- NX0U3H ‘notable pros thru cons:’
- NX0SH5 ‘per def’ ‘same or similar’ ‘sub’
- NX0T24 <0
- NX0T3U 0
- NWYSR5 >0 common (including suggested in here)
- NWYSVF ‘is-a’ including social parenting & subset
- NWYT4N has-a
- NWYSZT ‘instance-of’ probably especially when there are relation chains as in prototype-based programming
- NX0S4P ‘‘name’ ‘anew’’
- NX0S53 ‘reflexive partial order’
- NX0U18 ‘non-strict 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)
- ‘for remainder, sections overall’
- NX1GI7 ‘-’ ‘‘total order’’
- NX1GVA ‘notable pros thru cons:’
- NX1GXW ‘same or similar’ ‘sub’
- NX1GYX <0
- NX1H3U 0
- 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
- NX1GPI ‘‘name’ ‘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’
- NYHIAE ‘per def’ ‘same or similar’ ‘sub’
- ‘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
- 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.
- 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/lecture12-congclos.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
- 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/wp-admin/admin.php?page=pretty-link&search=5129&size=100 ends up with 12 entries; http://1.jothere.com/wp-admin/admin.php?page=pretty-link&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/wp-admin/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