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visits member for 2 years, 4 months
seen Aug 25 at 3:47

Aug
21
comment Which power means are constructible?
@Semiclassical, what's the source of this nice diagram, yours? The classical civilizations knew 10+ distinct means, as discussed here: tandfonline.com/doi/abs/10.1198/tast.2009.0006#.U_VjeIBdVRY. Are all described by line segments in a semicircle?
Apr
16
awarded  Yearling
Feb
27
comment Is the Green-Tao primes theorem true or pseudo-true?
@PeteL.Clark, As far as I know the only axiom in common to all branches of math, whether constructive or not, is the rule of deduction or Modus Ponens. Maybe you have an insider's view as to what the terminology of mathematical truth is- but I think any conclusion (B) is conditional on the truth of the assumption A (as well as the truth of the implication A-->B). Is there an alternative interpretation?
Dec
6
comment Reference Request on Order Theory topics
Roman's "Lattices and Ordered Sets" (2008) is good. If you browse the computer science shelves, you'll find a lot of topics on orders complementary to what's covered there, eg complexity of orders.
Nov
26
comment Why do imaginary numbers work (somewhat philosophical question)?
In the book "Schroedinger: Life and Thought", it's mentioned that he introduced complex phase to describe spin in his wave mechanics almost casually. Yet what a difference that innovation made.
Sep
3
comment Distinguishing equality and isomorphism as relations
@Rhubbarb, can you give an example and describe explicitly how that would distinguish equality vs. isomorphism?
Aug
20
comment smooth functions or continuous
@njguliyev, not to nitpick but I think it's relatively common to call Lipschitz continuous ODEs "smooth" - being just smooth enough for existence and uniqueness of solutions.
Jul
27
comment Famous uses of the inclusion-exclusion principle?
Bender and Goldman link is 404.
Jun
15
comment Edge in a convex polytope
@Lipschitz, check the "face lattice" section of en.wikipedia.org/wiki/Convex_polytope. The faces are ranked by dimension: extreme vertices (points) are 0-dim. Edges are 1-dim.
May
21
comment Questions on fractional Laplacian graph spectra
Chris, thanks for that. Curious how you discovered this, or is it a well known counterexample? ... I will visually compare the fractional spectra when I get a chance.
May
9
comment Truth of Fundamental Theorem of Arithmetic beyond some large number
@user14111 "Pure logic, and pure mathematics (which is the same thing)" - incidentally, Poincare' disagreed with Russell on this point. See eg "Great Feuds in Mathematics"
Apr
21
comment “Het” ternary and n-ary relations in $\bf Rel$?
Regarding the first claim, I take it a natural map relates the hom-sets you mention as well as $Hom_{Rel}(X \times Y,1)$. Re 2nd claim, does "respect" mean the same as preserve? To illustrate, can you provide a counterexample, say with X, Y, Z small finite sets?
Apr
21
comment “Het” ternary and n-ary relations in $\bf Rel$?
I understand "not to restrict to functions" - nevertheless functions are special relations, so what holds for relations must hold for functions... (By the way, a part from 1 is a point and a partition to 1 is also a trivial partition - I didn't state that explicitly above).
Apr
20
comment “Het” ternary and n-ary relations in $\bf Rel$?
+1 for the explanation - I've not seen this before in category books. But before I accept, if binary relation is specialized to function, I don't see how $X \times Y \to 1$ is the same as $1 \to X \times Y$. For example if the latter is an injection, it's a part of $X \times Y$, then the interpretation of the surjective dual is partition of that product set. Are these the same relation?
Apr
20
comment “Het” ternary and n-ary relations in $\bf Rel$?
Ok good poing about hom vs. het but what's a better pair of terms, endo vs. exo? that's not so known. - But, your comment seems inconsistent with Qiaochu's above, what am I missing?
Apr
20
asked “Het” ternary and n-ary relations in $\bf Rel$?
Apr
16
awarded  Yearling
Apr
9
comment The category Set seems more prominent/important than the category Rel. Why is this?
Marcel Erne' seems to argue (I think in his chapter "Closure" in Beyond Topology if I rem) that we should sort of switch points of view from Set to Order because he sees the lack of self-duality of Set as a limitation.
Apr
9
comment The category Set seems more prominent/important than the category Rel. Why is this?
This is interesting because in computer science and relational databases (RDBMS) partial functions are more relevant than total functions.
Apr
6
comment Can a Partial Order be symmetric in addition to its properties?
@julien, keeping in mind that order has "=" built into its definition, so defining equality in terms of a relation that already defines equality is impredicative. Isomorphism "~" should be substituted. So it's not that simple.