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Lenar Hoyt
  • Member for 10 years, 8 months
  • Last seen more than a month ago
8 votes
3 answers
431 views

Why is the universal quantifier $\forall x \in A : P(x)$ defined as $\forall x (x \in A \implies P(x))$ using an implication?

6 votes
4 answers
205 views

Find a sum of appropriate values of $\cos$ and $\sin$ to determine the value of a series

6 votes
2 answers
5k views

What's the difference between the associative law and the commutative law?

5 votes
6 answers
6k views

How can I prove the inequality $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} \geq \frac{9}{x+y+z}$?

5 votes
3 answers
3k views

How can I prove that the binomial coefficient ${n \choose k}$ is monotonically nondecreasing for $n \ge k$?

4 votes
2 answers
125 views

Are there any trivial examples of languages that cannot be produced by formal grammars?

3 votes
1 answer
89 views

How to prove $f(n) := \frac{1}{2}(a+(f(n-1))^2) ≤ 1-\sqrt{1-a}$

3 votes
1 answer
4k views

I'm confused: does # mean Q.E.D. or contradiction?

2 votes
1 answer
137 views

How can I prove this equation: $(1+ \frac{1}{n})^n = 1+ \sum\limits_{k=1}^n{\frac{1}{k!}}1(1-\frac{1}{n})\cdot(1-\frac{2}{n})…(1-\frac{k-1}{n})$ [duplicate]

2 votes
2 answers
191 views

Solutions to $z^3 - (b+6) z^2 + 8 b^2 z - 7+b^2 = 0, b\in \mathbb R, z \in \mathbb C$

1 vote
1 answer
61 views

What is the easiest and fastest way to produce a uniformly distributed random number between 0 and 9 off the cuff?

1 vote
1 answer
113 views

How can I find the largest axis-parallel square that can be inscribed into a linearly transformed unit square?

1 vote
1 answer
120 views

Why is $\frac{d f(g(h(x)))}{d x} = \frac{d f(g(h(x)))}{d h(x)}\frac{d h(x)}{d x}$, not $\frac{d f(g(h(x)))}{d g(h(x)))}\frac{d h(x)}{d x}$?

1 vote
3 answers
140 views

How can I prove that $f(x):=\frac{1}{1+x\cdot\left|x\right|}$ is not bounded above?

1 vote
1 answer
1k views

Understanding stereographic projection in fish-eye lenses

0 votes
3 answers
342 views

Why is $1 + 1 = 0$ in $\{0, 1\}$?

0 votes
4 answers
125 views

How can I calculate the partial derivative $\frac{\partial}{\partial \vec{x}} f\left(A\vec{x} + \vec{b}\right)$ using matrix calculus?

0 votes
0 answers
53 views

Why are $x$ and $y$ independent conditioned on $z$ if $p(x,y|z) \propto p(z|x)p(x)p(y|z)$?

0 votes
2 answers
96 views

Does the central limit theorem apply for random variables with densities which are not asymptotic?