Carl Mummert

Marshall University

science.marshall.edu/mummertc

Age: 36

I work in mathematical logic. My main areas of interest are arithmetic, reverse mathematics, computability, and proof theory.
3h
awarded Constituent
8h
comment Good source on current 'views and thoughts' on mathematics
That I am not sure about - most of the rephrasings I can think of only make the question seem more philosophical.
8h
comment Good source on current 'views and thoughts' on mathematics
Perhaps it is just the way that the question is phrased (this may also be why there are not many answers). It seems to me the question is more philosophical than mathematical - and such questions often attract users who want to express their own opinions. @user2520938
9h
comment Problems taking the limit in $\int_a^b f=\lim_{c\to a}\int_c^b f$ from definitions
Isn't this equivalent to $\lim_{c \to a^+} \int_a^c f(x)\,dx = 0$,using the additivity of the integral? The formula I stated may be easier to prove, using the fact that the function is bounded. (There is a deleted answer to this effect.)
10h
revised Proving Infinite Ramsey's theorem
added 60 characters in body
10h
revised Proving Infinite Ramsey's theorem
edited body
10h
answered Proving Infinite Ramsey's theorem
1d
comment How can it be decidable whether $\pi$ has some sequence of digits?
@Shagun: if $N$ exists, it is just a natural number, and every natural number is computable (because we can just hard-code it).
Dec
15
comment Are the real numbers really uncountable?
I see. I was thinking of the way that we often only have a partial definition. For example, we may talk about a real that is irrational, or that is in the closure of some set, or that is in a particular $G_\delta$ set. This gives us enough information to work with the real, but not enough to define it individually. @Dan Piponi
Dec
15
answered Is there a concise way to notate 'There are exactly 482 x, such that Px...' in logical notation?
Dec
15
comment Are the real numbers really uncountable?
"Every real number must have a definition to be discussed" - why is that the case?
Dec
14
awarded Nice Answer
Dec
14
comment 2014 Moderator Election Q&A - Question Collection
The wording of this might be tweaked a little. On this site, we have a strong prejudice against binding votes, except for clear cases of vandalism, spam, etc. So the real question, I think, is to ensure the candidate is aware of this practice and the reasons for it. The wording of this question suggests we have a bunch of current moderators casting binding votes on questions they've edited.
Dec
14
comment A travesty of upvoting
I don't think Fermat's Little Theorem is required to tell that $2^4$ is congruent to $1$ modulo $5$, or that $6 \times 6 = 36$ which also ends in $6$. There is rigor, and then there is unneeded rigor...
Dec
13
comment Review info on candidates
Do you mean the fake reviews that are sometimes presented to trick reviewers, with the message "That was only a test"? I would not give those any weight, because the "correct" choice according to the software is often wrong.
Dec
13
comment If $f$ and $g$ are continuous, then max(f, g) is continuous and differentiable
@1234: please don't make so many trivial edits so quickly!
Dec
13
comment How to prove $S=\{(x,y) \in \mathbb{R}\times \mathbb{R}|x - y \in \mathbb{Q} \}$ is an equivalence relation?
In general, you can prove many undergraduate-level problems in this way, by asking "What do I need to prove?", then "What does that really mean?", then "So what do I need to do to prove that?", then "What does that mean, in other words?", and so on. You keep rewriting the problem into smaller and smaller pieces until you reach pieces that are small enough to handle directly.
Dec
13
answered How to prove $S=\{(x,y) \in \mathbb{R}\times \mathbb{R}|x - y \in \mathbb{Q} \}$ is an equivalence relation?
Dec
13
revised How to prove $S=\{(x,y) \in \mathbb{R}\times \mathbb{R}|x - y \in \mathbb{Q} \}$ is an equivalence relation?
added 13 characters in body; edited title
Dec
13
revised proof with mapping reduction to Htm ,that p is undecideable
edited tags
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