mcb

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13 Questions

views newest activity votes

6

votes

4

answers

149

views

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

sequences-and-series

jan 5 '12 at 7:35 mcb 291

1

4

votes

6

answers

440

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

apr 10 at 12:01 chilchin 51

3

votes

2

answers

43

views

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

formal-languages formal-grammar

may 11 at 12:10 zyx 11.1k

3

votes

3

answers

371

views

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

sequences-and-series binomial-coefficients

dec 4 '11 at 4:27 Srivatsan 15.6k

3

votes

1

answer

245

views

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

notation

nov 20 '11 at 23:03 Zev Chonoles 54k

3

votes

1

answer

81

views

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

analysis

nov 15 '11 at 18:13 mcb 291

1

3

votes

1

answer

268

views

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

abstract-algebra

oct 24 '11 at 20:22 Alon Amit 6,161

2

2

votes

2

answers

87

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

may 13 '12 at 14:01 Zarrax 19.7k

2

votes

1

answer

87

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

nov 14 '11 at 20:50 Arturo Magidin 158k

1

vote

1

answer

54

views

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

logic definition quantifiers

may 21 at 19:06 ZettaSuro 883

1

vote

2

answers

84

views

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

real-analysis

nov 25 '11 at 21:41 Srivatsan 15.6k

1

1

vote

1

answer

227

views

Understanding stereographic projection in fish-eye lenses

geometry projective-geometry

nov 5 '11 at 1:44 Henning Makholm 53.6k

-1

votes

3

answers

312

views

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

abstract-algebra

oct 25 '11 at 7:35 user7530 8,253

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