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Jan
31
answered Defining natural transformations based on generalized elements?
Jan
31
comment Defining natural transformations based on generalized elements?
When you express a doubt about the existence of "this morphism" in $\mathbf{C}$, which morphism in particular do you mean?
Jan
20
comment Convention about distinctness of the elements of a set
There's no reason to assume that they must be distinct. In the case $a=b$, for instance, all that means is that $\{a,b,c\}=\{a,a,c\}=\{a,c\}$. The main thing we're doing writing the variables distinctly is allowing that the set may contain as many as three things.
Dec
21
comment Examples of Partial Combinatory Algebras with surjective pairing?
@tci: It's a monoid that is Cartesian closed except that it has no terminal object. It's the general class of structure that works as a model of untyped lambda calculus with surjective pairing.
Dec
10
comment Do mathematicians ever prove that something can or can't be proved?
@Servaes: I meant a proof in the object language. I may be able to show in our meta-theory that something holds of all groups (or whatever) and that this something is a first order property without ever writing a proof in the language $\mathcal{L}=\{e,-^{-1},\cdot\}$.
Dec
10
answered Do mathematicians ever prove that something can or can't be proved?
Dec
8
asked Examples of Partial Combinatory Algebras with surjective pairing?
Dec
6
comment What does this ∩ symbol mean in terms of geometry
Can you give more context on how you saw it used?
Dec
6
comment How big can a set be?
There is a largest cardinal in NF and like theories, but generally no.
Dec
4
answered How does one prove transfinite induction in ZFC?
Dec
3
comment “A Category Object in another Category”?
@Udit: A category with one object is a monoid. A category with only isomorphisms is a groupoid. A group is a category that's both a monoid and a groupoid.
Dec
3
answered “A Category Object in another Category”?
Dec
2
revised Assume that $S=\{(x,y): x-y=0\}$. Find the projection formula $P_S$.
Improving the formatting of the title. Looked okay when viewing the question, but odd on the front page.
Dec
2
comment Notation with a colon that looks like set notation - what is it?
Have you seen the same thing with $\mid$ instead of $:$? They mean the same thing.
Nov
30
accepted Replacement in a topos with an eye to a natural model of TST
Nov
29
comment Replacement in a topos with an eye to a natural model of TST
Ah, so that is not so far off from my hunch, but definitely less brutish. I may finally be developing some small sense for indexed categories after all...
Nov
28
comment Assumptions at Primordial Math
@MarcPaul: Dan has given a second order induction scheme, which I believe does prove Goodstein's theorem. It is certainly true that the first order Peano axioms won't.
Nov
28
comment Transitive Closure and Composite relations in set builder notation
@Mirko: I'm so used to more abstract contexts that I didn't even think of that very nice solution for integers.
Nov
28
answered Transitive Closure and Composite relations in set builder notation
Nov
28
comment Transitive Closure and Composite relations in set builder notation
Well, you can get a binary relation back out by removing one of the variables from the triple and putting a quantifier in front of the defining formula. But the transitive closure is actually a bit more complex. I suppose I'll write up an answer, actually.