User Lenar Hoyt

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?

asked May 21, 2013 at 18:56

6 votes

4 answers

205 views

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

sequences-and-series

asked Jan 5, 2012 at 5:46

6 votes

2 answers

5k views

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

abstract-algebra

asked Oct 24, 2011 at 19:56

5 votes

6 answers

6k views

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

algebra-precalculus inequality

asked Nov 3, 2011 at 0:59

5 votes

3 answers

3k views

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

sequences-and-series inequality binomial-coefficients

asked Dec 4, 2011 at 0:37

4 votes

2 answers

125 views

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

formal-languages formal-grammar

asked May 11, 2013 at 11:34

3 votes

1 answer

89 views

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

analysis

asked Nov 14, 2011 at 22:21

3 votes

1 answer

4k views

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

notation

asked Nov 20, 2011 at 21:23

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]

algebra-precalculus

asked Nov 14, 2011 at 20:32

2 votes

2 answers

191 views

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

algebra-precalculus polynomials complex-numbers

asked May 13, 2012 at 8:30

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?

recreational-mathematics

asked Jan 18, 2014 at 2:02

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?

geometry linear-transformations

asked May 10, 2017 at 8:40

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 $\frac{d f(g(h(x)))}{d g(h(x)))}\frac{d h(x)}{d x}$?

calculus derivatives chain-rule

asked Nov 9, 2015 at 23:06

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?

real-analysis

asked Nov 25, 2011 at 20:41

1 vote

1 answer

1k views

Understanding stereographic projection in fish-eye lenses

geometry projective-geometry

asked Nov 5, 2011 at 0:45

0 votes

3 answers

342 views

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

abstract-algebra

asked Oct 24, 2011 at 21:29

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?

matrix-calculus

asked Mar 21, 2016 at 14:49

0 votes

0 answers

53 views

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

probability

asked Oct 28, 2016 at 13:32

0 votes

2 answers

96 views

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

statistics central-limit-theorem

asked Feb 8, 2014 at 14:50

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19 Questions

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

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

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

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

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

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

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

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

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]

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

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

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

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 $\frac{d f(g(h(x)))}{d g(h(x)))}\frac{d h(x)}{d x}$?

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

Understanding stereographic projection in fish-eye lenses

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

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

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

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