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Apr
17
comment Need help with proof of existence of $\sqrt{2}$
You seem to already assume quit a lot about $\sqrt 2$....
Apr
17
answered Need help with proof of existence of $\sqrt{2}$
Apr
16
comment What are some illustrative examples that demonstrate how $\succ$ can differ in behavior from $>$ and/or $\geq$?
note that in the reference the well-below relation is the classical one from domain theory, i.e., it talks about directed sets. Flagg's notion is slightly more general.
Apr
16
answered What are some illustrative examples that demonstrate how $\succ$ can differ in behavior from $>$ and/or $\geq$?
Apr
15
comment Looking for info on power set functor
and I suggest again: you may be interested in topos theory.
Apr
15
answered Consider the following expression about natural number: $\forall n\exists m: m^{2}=n$
Apr
15
answered Does set theory help understand machine learning or make new machine learning algorithms?
Apr
15
answered Why/How are there infinite points in a line segment?
Apr
14
comment Are clopen sets Borel?
you state yourself that open sets are Borel. So certainly clopen sets are Borel.
Apr
12
answered if there is an injection between $A$ and $B$, does there exists an injection between $P(A) $ and $P(B)$?
Apr
12
comment Proving the set identity $(X \cup Y) = X + Y - (X \cap Y)$
You need to be precise about how you model sets with repetition, and then how you define the set operations, and the meaning of equality. Before you do that, the question is too vague (though certainly there is a grain of truth to it).
Apr
12
answered Can a non-constant analytic function have infinitely many zeros on a closed disk?
Apr
11
answered Every nonprincipal ultrafilter on $\omega$ is uncountable.
Apr
11
comment Deriving the value of $\pi$ from a dart board
You can run a one-line R code that will simulate this approach. You'll find that you need about 100,000 darts to get $\pi$ correct to about 2 decimal places. This method is quite inefficient, though cool.
Apr
10
comment Can we get categories like $\mathbf{TopGrp}$ as some kind of a pullback?
sorry, I was on auto-pilot. For abelian groups this works because finite products agree with finite coproducts, but now change from abelian groups to groups and it stops working since the coproduct is much larger than the product.
Apr
10
comment Why is delta used to describe difference between two entities
$\Delta$ifference.
Apr
10
comment Can we get categories like $\mathbf{TopGrp}$ as some kind of a pullback?
@goblin consider $F:Set\to Ab$, the free abelian group functor, left adjoint to $U$. Now consider both categories as multicategories via the cartesian product. Then, denoting $*$ any singleton set,$Set(*, *; UA)\cong UA$ for any abelian group $A$ while $Ab(F*, F*;A)$ is considerably different, so there isn't even a bijection, let alone a natural isomorphism. This happens for many other free construction, so this definition, while it logically makes sense, suffers from a severe lack of examples.
Apr
10
revised Prove that $\det(AA^T+I)\ge 1$
edited body
Apr
10
comment Proof of infinite primes
@MurtuzaVadharia you have been given a value for $n$ such that neither is prime. What else do you want?
Apr
10
comment Proof of infinite primes
see the comments to your question.