Reputation
4,392
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
2 15 30
Newest
 Nice Answer
Impact
~85k people reached

1d
answered Neural Network Sigmoid Problem
Feb
4
comment Show that if a bipartite graph $G = (V, E)$ with bipartition $V = A \cup B$ is $k$-regular, then $|A| = |B|$.
Drawing a picture might help
Feb
4
answered Show that if a bipartite graph $G = (V, E)$ with bipartition $V = A \cup B$ is $k$-regular, then $|A| = |B|$.
Feb
2
comment Find the closed form for the double sum $ \sum_{1\leq j \leq k \leq n }3^k=\sum_{j=1}^n \sum_{j=k}^n 3^k$
Should $j$ appear in the summand? If not, this becomes $\sum_{1 \leq k \leq n} k 3^k$ since each term $3^k$ appears $k$ times, once for each $1 \leq j \leq k$.
Jan
24
answered How to use a proof by contradiction in group theory!
Jan
5
comment Book for studying Calculus I
Stay away from books with "advanced calculus" or "real analysis" in the title unless you know that's what you're looking for. These ones give you a much more rigorous, proof-heavy exposition of calculus that would be very difficult for most beginning calc students.
Dec
30
comment Proving $x=f^n(x)$ for some $n\in \mathbb{Z}$
I think we must require $n> 0$, or else the problem is trivial. But then the statement is not always true if $A$ is not finite, as Jendrik points out. So I would check the exact wording of the question. So I would say there was a mistake in the original question, or else you have communicated it incorrectly here.
Dec
28
awarded  Nice Answer
Dec
27
answered What are some math books written in dialogue or story form, e.g., a teacher explaining to a student?
Dec
24
comment Past open problems with sudden and easy-to-understand solutions
See also: Examples of open problems solved through short proof
Dec
9
comment Does $\infty$ mean $+\infty$ in “English mathematics”
Yes, $\infty$ usually means $+\infty$ in the context of real numbers.
Dec
6
comment Young diagram for $S_5$
Looks good. If you want the dimensions of the irreps, you can list out all of the standard young tableaux of the given shape.
Dec
5
comment Young diagram for $S_5$
Each irrep will correspond to a partition of 5. So the $7$ associated partitions are $5$, $41$,$32$,$311$,$221$,$2111$,$11111$. If you count the number of standard young tableaux for each of these shapes you will get the dimension of each irrep.
Dec
5
comment Young diagram for $S_5$
Is this a homework question? It might help if you state the problem.
Dec
5
comment Young diagram for $S_5$
It's not clear what you are trying to do here. Each irreducible representation of $S_5$ is associated with a partition and young diagram, but what is the "young diagram of $S_5$"? Why do you need to make it into a young tableau?
Dec
4
answered prove $A=B \iff A \times A = B \times B$
Dec
4
comment Prove that $f(x):\mathbb{R}\to\mathbb{R}$ , $x \mapsto x^3$ is injective.
Any strictly increasing function is injective. Do you see why?
Dec
2
reviewed Reject Easy way of memorizing values of sine, cosine, and tangent
Dec
2
reviewed Approve Easy way of memorizing values of sine, cosine, and tangent
Dec
2
revised Prove any polynomial of degree n that is orthogonal to ${1, x, …, x^{n-1}}$ is a constant multiple of a Legendre Polynomial.
edited body