Reputation
21,288
Top tag
Next privilege 25,000 Rep.
Access to site analytics
Badges
4 52 121
Newest
 Good Answer
Impact
~513k people reached

Apr
26
comment “Spatial (geometrical)” realization of Elementary topos?
In that case, I would liken finitely cocomplete categories to abelian groups.
Apr
26
comment “Spatial (geometrical)” realization of Elementary topos?
Complete categories are analogous to Abelian groups? Can you explain a bit more? I could say "cocomplete categories are analogous to sup-complete lattices", for instance, and that makes sense to me. I am curious how you get to Abelian groups.
Apr
25
comment Function that gives 1 only when an integer is divisible by another integer
Excellent, I am glad to see the trick is useful outside of a desert as well.
Apr
25
comment Function that gives 1 only when an integer is divisible by another integer
What exactly does "in practice" mean here? Like, if you're in the desert and need to figure out whether 15485863 divides 2778545904897799?
Apr
25
comment What is the Cantor-Bendixson rank of the space of first order theories?
What was in Dana Scott's PhD thesis? I never saw it but I think it was about metric completions of theories, so perhaps there are results about the Cantor-Bendixson rank as well?
Apr
18
comment Understanding Strong Normalization for Identity Types in Martin-Löf Intensional Type Theory
Also, this is not a research-level question. It is more suitable for math.stackexchange.com or cs.stackexchange.com.
Apr
18
comment Understanding Strong Normalization for Identity Types in Martin-Löf Intensional Type Theory
Once you tell us what $w$ is we will be able to reduce $t$, yes. Until then it's a secret.
Apr
12
comment An inequality on the simplex involving $x^x$
Is this the sort of idel curiosity that lead to the discovery of so many things, or a question motivated by a "real problem"? (I am asking out of idle curiosity because I can't image how and why anyone would think of these inequalities.)
Apr
12
answered Coproducts and “Error Conditions” in Math vs CS
Apr
11
comment Current status of computable spectral theorem and interpretation of quantum mechanics
Corollary 15 does not state that the basis can be computed from the matrix. It is a non-uniform theorem: for every computable matrix there exist such-and-such basis, but there is no algorithm that passes from one to the other. So, Corollary 15 is in fact correct and you misread it - nowhere does it claim that the $x_i$ are computable functions.
Apr
7
comment Identity types: What makes Intuitionistic Type Theory *intuitionistic*?
@SimonHenry: no. That's like saying that idempotents in groups are explained by the cyclic group of order 7 because that group has some idempotents.
Apr
7
answered Identity types: What makes Intuitionistic Type Theory *intuitionistic*?
Apr
7
comment Identity types: What makes Intuitionistic Type Theory *intuitionistic*?
By "intuitionistic explanation" do you mean something like a BHK informal semantics?
Mar
12
comment Can Turing machines clarify mathematical, philosophical, and physical existence?
Perhaps you're just asking about reverse mathematics? Have a look at en.wikipedia.org/wiki/Reverse_mathematics where it is explained that Gödel's completeness theorem follows from weak König's lemma $\mathsf{WKL}_0$ (over the base theory $\mathsf{RCA}_0$).
Mar
12
comment A question on the consistency of a (seemingly) very weak set theory
I think the worry about inconsistency comes from the fact that changing your inference rule to the axiom $\forall a . (\alpha(a) \Leftrightarrow a \not\in \lbrace x \mid \lnot \alpha(x) \rbrace)$ opens the road to Russell's paradox.
Mar
12
comment A question on the consistency of a (seemingly) very weak set theory
May terms $\lbrace x \mid \alpha(x) \rbrace$ contain parameters?
Mar
12
comment Can Turing machines clarify mathematical, philosophical, and physical existence?
It's a bit strange to equate consistency with existence, as then at the very least we have to believe in existence of mutually incinsistent entitites. In any case, I do not understand what is being asked here. It sounds as if you are asking about the logical complexity of Gödel's completeness theorem (every consistent first-order theory has a set-theoretic model), or maybe what it takes to prove it?
Mar
12
comment “Kolmogorov complexity” of models of computation
I think you need to explain what a computational model is and what it means for one fo them to interpret another, or more generally what a morphism between computational models is. For instance, you could say that a computational model is a partial combinatory algebra and a morphism is Longley's applicative morphism.
Feb
9
comment Can we do better than zero padding of FFT?
With all respect to the OP, can someone rewrite the question into more standard mathematical terminology so that we can tell what it is about?
Feb
6
comment What (fun) results in graph theory should undergraduates learn?
This question is not about math research. It belongs to matheducators.stackexchange.com, please move it there.