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Eevee Trainer
  • Member for 3 years, 9 months
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28 votes
9 answers
1k views

Various ways to calculate $\int \sin(x) \cos(x) \, \mathrm{d}x$

19 votes
5 answers
4k views

A curiosity: how do we prove $\mathbb{R}$ is closed under addition and multiplication?

13 votes
3 answers
3k views

Numbers such that they equal the product of their own digits

13 votes
9 answers
406 views

Determinants of matrices defined by the minimum/maximum indices of their entries

9 votes
1 answer
239 views

How does one solve for $x$ in the equality $a^x = bx + c$?

8 votes
1 answer
428 views

Proving the pullback of monics is monic.

7 votes
1 answer
124 views

Solution verification: Showing that $\|A\|_\infty = \max_{1 \le i \le n} \sum_{k=1}^n |a_{i,k}|$ for $A \in \Bbb R^{n\times n}$

7 votes
1 answer
137 views

Showing a biconditional statement about function lim sups in $\Bbb R^n$, and codifying the intuition into a proof

6 votes
2 answers
289 views

Visualizing the norm of a bounded linear functional

6 votes
5 answers
263 views

Showing $f(t) = t^4 + 2t^2 + 9$ is reducible over $\Bbb Q$

6 votes
1 answer
121 views

Definitions of the Stratonovich integral and why the "average" definition is arguably correct

5 votes
2 answers
244 views

What is the difference between "$=$" and "$\equiv$"?

5 votes
1 answer
81 views

Proof verification: An arrow which is monic under a faithful functor is itself monic

5 votes
2 answers
2k views

Why is the negation of the statement $\exists x P(x)$ given by $\forall x (\neg P(x))$ and not $\not \exists x P(x)$?

5 votes
2 answers
432 views

Riemann-Stieltjes integral of a continuous function w.r.t. a step function

5 votes
1 answer
142 views

Showing a summation identity for $1$, possibly tied to Legendre polynomials

4 votes
1 answer
60 views

Given a particular matrix $A \in \operatorname{GL}_n(F)$, what is an easy way to determine $A^n$ $\forall n \in \Bbb Z$?

4 votes
2 answers
147 views

Completing a proof on integrability: $f$ is Riemann integrable under the mesh definition iff $\sup L_\Gamma = \inf U_\Gamma$

4 votes
4 answers
112 views

Why do the vertices of $f(x) = ax^2 + bx + c$, when fixing $a$ and $c$ but varying $b$, lie on $g(x) = -ax^2 + c$?

4 votes
1 answer
201 views

Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$?

4 votes
3 answers
102 views

Constructing an isomorphism of group products

4 votes
1 answer
249 views

A quick question about complex integrals and Cauchy's integral formula

4 votes
1 answer
88 views

How to solve a specific complex integral: $\int_M \frac{(6z+1)^5 \cos(3z+1)}{(3z+1)^2}dz$

3 votes
3 answers
216 views

$Set$, $Set^{op}$, categorical properties, and proving why these categories aren't isomorphic.

3 votes
1 answer
291 views

Proof sketch/verification - proving a pullback in a diagram is an equalizer.

3 votes
1 answer
277 views

Why do we have the present order of operations, and how do hyperoperations fit in?

3 votes
1 answer
664 views

Is there a connection between $\zeta(-1)$ and Ramanujan's calculation of the sum over $\mathbb{N}$?

3 votes
1 answer
58 views

Generalizing the apothem characterization of area for regular polygons, to convex regular polyhedra (and more?).

3 votes
1 answer
103 views

Showing $\sum_{k=0}^{n+1} \binom n k \frac{(-1)^k}{(n+k)(n+k+1)} = \sum_{k=0}^{n+1} \binom {n+1} k \frac{ (-1)^k}{n+k}$

3 votes
1 answer
41 views

Continuity of a bilinear form on $H^1(0,2)$