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| visits | member for | 1 year, 1 month |
| seen | 22 hours ago | |
| stats | profile views | 483 |
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1d |
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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. |
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May 9 |
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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" |
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Apr 21 |
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“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? |
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Apr 21 |
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“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). |
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Apr 20 |
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“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? |
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Apr 20 |
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“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? |
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Apr 20 |
asked | “Het” ternary and n-ary relations in $\bf Rel$? |
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Apr 16 |
awarded | Yearling |
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Apr 9 |
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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. |
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Apr 9 |
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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. |
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Apr 8 |
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Why metric space is topological space and examples of non-Hausdorff spaces See also: Are all metric spaces topological spaces? |
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Apr 6 |
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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. |
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Apr 6 |
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Can a Partial Order be symmetric in addition to its properties? @julien, I'm sayin, do you think the Wikip. article is correct that equality is the only such relation, or is isomorphism also both an equivalence and an order? I maintain that isomorphism would have to be substituted for equality also in the definition of order and so also satisfies that "equation". |
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Apr 6 |
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Complex numbers with conjugate multiplication - field or …? Do my subsequent comments resolve your: "It does not subtract them, it adds their opposites"? |
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Apr 6 |
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Can a Partial Order be symmetric in addition to its properties? @julien, as discussed in this Q, Wikipd. entry for equality relation states that it is the only relation that is an equivalence and an order. However the definition is impredicative and isomorphism also seems to satisfy that proposition when correctly substituted. Maybe you can shed some light? "Diagonal" seems ok as a descriptor however. |
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Apr 6 |
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Complex numbers with conjugate multiplication - field or …? @julien, then...? |
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Apr 6 |
accepted | Complex numbers with conjugate multiplication - field or …? |
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Apr 6 |
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Complex numbers with conjugate multiplication - field or …? Jonas is right, that's what I'm asking. |
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Apr 6 |
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What is the relative behaviour when a center circle surrounded by 6 circles is (recursively) replaced by 6 circles I think blue circles is initial state (k=0), and red circles are after one replacement (k=1). He'd like to know the asymptotic behavior as k grows. |
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Apr 2 |
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Is there a way to axiomatize the category of sets and relations? @QiaochuYuan, (1) the cat I described is called $\bf Rel$ in the publication that I based my answer on (can email you the photo in my iPhone but there's no biblio info). If this is not the "category of sets and relations" what's the diff and relationship between them? (2) Isn't axiomatization just definition? |
