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comment What are some applications of elementary linear algebra outside of math?
Today, PageRank is vastly more compplicated with hundreds of "signals" (and new ones added all the time) and revisions to the algorithms - mostly to address the endless war on SEO: en.wikipedia.org/wiki/Search_engine_optimization.
Dec
17
comment What are the most overpowered theorems in mathematics?
...the basis of Probability and Statistics applicable only when the assumptions are satisfied. In particular when independence is violated, CLT can fail badly in the real world - as opposed to what Savage called small world, and what Taleb called Ludic, ie games or toy systems.
Dec
9
comment Logical relations between relations
en.wikipedia.org/wiki/Relation_algebra, also en.wikipedia.org/wiki/Logical_matrix
Dec
9
comment Associativity for Magma
@IttayWeiss, The whole purpose of associahedra is to study associativity, just find the right operad > en.wikipedia.org/wiki/Operad_theory#Associative_operad
Dec
9
comment Associativity for Magma
@IttayWeiss, on p.11 of Mueller-Hoissen et al "Associahedra, Tamari Lattices..." says: a binary operation on a set is n-associative if any monomial composed of n+1 elements is independent of paraenthesization... For a partial binary op (..partial magma)...
Dec
8
comment Associativity for Magma
@IttayWeiss, you wrote "There are no easy visual criteria". How much visual do you want than polytopes, at least in low dimensions. Asssociahedra also bear relation to permutohedra, displaying a geometric link b/w associativity and commutativity.
Dec
8
awarded  Caucus
Dec
6
comment In (relatively) simple words: What is an inverse limit?
@MartianInvader, "The inverse limit X is a subset of the product of the X_i". Since a (2-valued) binary relation in set theory is a subset of products of two sets, then is an inverse limit an infinite-arity relation?
Dec
6
revised Visual\Geometric characterization of associativity
added 90 characters in body
Dec
6
answered Visual\Geometric characterization of associativity
Dec
6
comment Associativity for Magma
@IttayWeiss, there is a geometric interpretation via commutativity on Stasheff polytopes aka en.wikipedia.org/wiki/Associahedron
Dec
5
comment On “familiarity” (or How to avoid “going down the Math Rabbit Hole”?)
+1, but this prescription seems to leave out a modern view point what MacLane described as the protean nature of math: sume and product means different things in different forms. Eg non-negative and cone-preserving matrices and their link to combinatorial geometry. In which case the order properties of the field greatly extend the expressiveness of vector space. Looking at math chronology, quaternions, octanions and one more level could also be substituted in the vector space.
Dec
5
answered Results that came out of nowhere.
Nov
27
comment Proof of Ramsey Theorem with explicit use of AC
Not trying to badger you Asaf, I didn't see a context established, as Ramsey theory is so general.
Nov
27
comment Proof of Ramsey Theorem with explicit use of AC
Yet, the ring of integers is countable but not well-ordered.
Nov
27
comment Proof of Ramsey Theorem with explicit use of AC
"Countable sets are well-ordered". Integers are not well-ordered: en.wikipedia.org/wiki/Well-order#Integers
Nov
23
comment What are the main uses of Convex Functions?
@littleO, a convex hull is the join of affine and cone hulls, and linear span is the meet. In higher dimensions cones can be more than one-sided, eg positive orthant in R^3 is a cone. Similarly, a triangle has 3 sides, intersections of that cone and an affine plane.
Nov
23
comment Defeating Russell's paradox
@beginner, fyi: I remember at least Goldblatt in Topoi and Awodey in Category Theory mention Russell paradox in relation to categories, so it is not just a problem in set theory.
Nov
22
comment Dilemma for Studying Probability Theory while Waiting to Learn Measure Theory
@TaxxiDriver, physicist ET Jaynes in his book Probability Theory more or less states that measure theory has no impact on statistics. Also, Renyi's book is good at least the back on information theory re generalized Shannon entropy.
Nov
16
comment What is the most influential work of Grothendieck in mathematics?
colinmclarty.com/Grothendieck.html