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1h
comment Logical consequence of Euclid's theorem
Gödel numbering-like methods may rely on the infinitude of the set of primes
3h
awarded  Nice Answer
3h
answered Prove A Group is Not Simple
4h
comment Technical name for an almost-monotonic function
Alternative condition: There exists monotonic $g$ with $\|f-g\|_\infty\le\epsilon/2$
4h
comment Does the definition of the fundamental group implicitly assume the Axiom of Choice?
Do we make a choice at all? After all, the result does not depend on it, so we have no choice how to define $\circ$. Put differently: Assume we have a set $S$ and an equivalence relation $\sim$ on it and an index set $I$ and a map $F\colon S^I\to T$ such that $(\forall i\in I\colon f(i)\sim g(i))\to F(f)= F(g)$. Do we need choice to define $F/{\sim}\colon (S/{\sim})^I\to T$?
7h
answered Sum of super exponentiation
9h
comment What's a group whose group of automorphisms is non-abelian?
Of course the real question was not to name such a group, but to describe how to find such a group. I find it natural to try the simplest example of a nonabelian group ($S_3$) and try to ensure that $S_3$ is a subgroup ioof the automorphism group. As permuting things is the favorite pastime of $S_3$, something like above might jump to your mind.
9h
answered What's a group whose group of automorphisms is non-abelian?
9h
answered Jimmy got a 38.5% (± 0.05%) on his math test. How many questions did the test have at a minimum?
10h
comment If I flip a coin 1000 times in a row and it lands on heads all 1000 times, what is the probability that it's an unfair coin?
The Finland 1 penni of 1969 weighs just 0.45g :) -- But I guess there are only about $10^{15}$ coins in the world (this discussion ends up with about $2\cdot 10^{12}$ coins in the US).
14h
answered Proof the series is finite using following inequality
14h
revised Proof the series is finite using following inequality
added 126 characters in body
14h
comment Show that the sum of (outdeg(v)-indeg(v))=0
Or note that $$\sum_{v\in V}(\operatorname{outdeg}(v)-\operatorname{indeg}(v))=\sum_{v\in V}(\sum_{w,vw\in E}1-\sum_{w,wv\in E}1)=\sum_{vw\in E}1-\sum_{wv\in E}1=0 $$
16h
comment Sum of super exponentiation
It is unlikely that the period is much smaller. Try dynamic programming
16h
answered Is my example of non equivalent maps correct?
1d
answered limit and infinite ordinals: same thing?
1d
comment Issue with associativity of group
@MattSamuel Virtually all weird group operations on (subsets of) $\mathbb R$ that are posed as exercise can be solved by exhibiting an isomorphism such as here - but often it is easier to guess. With this in mind, and assuming a Möbius transform as $f$, I noted that subtract one, take reciprocals, subtract one would at least map the interval to the positive reals, i.e., a set that we recognize as a standard group. And - surprise, surpirise - the bijection turns out to be an isomorphism ...
1d
comment In what structures does $ (-1)^2 = 1$?
@Gil-Mor Repeat: Not groups
1d
answered Prove $\exists$ $v \in V$ so that $(v , f(v))$ is a basis of $V$
1d
answered Power set of $\{\emptyset,\{\emptyset\}\}$