Question

Prove that for any polynomial $P(x)= a_nx^n + \cdots +a_1x+a_0,P$ is differentiable

score 130 · Answer 1 · 2015-11-09 21:23:59

130

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Prove that for any polynomial $P(x)= a_nx^n + \cdots +a_1x+a_0,P$ is differentiable

Published on 09 Nov 2015 - 21:23

score 119 · Answer 2 · 2015-11-10 06:47:25

119

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Is $H$ the Commutator Subgroup of $G$ if $H\neq \{1\}, H\leq G$ and $[H, G] = [H, H]$?

Published on 10 Nov 2015 - 6:47

score 2.6k · Answer 3 · 2015-11-10 21:16:20

2.6k

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Every function $f:\mathbb{N}\rightarrow\mathbb{R}$ is continuous (using definition)

Published on 10 Nov 2015 - 21:16

score 126 · Answer 4 · 2015-11-10 21:54:27

126

Views

Prove $ \forall x >0, \quad \sqrt{x +2} - \sqrt{x +1} \neq \sqrt{x +1}-\sqrt{x}$

Published on 10 Nov 2015 - 21:54

score 1.4k · Answer 5 · 2026-04-03 18:18:20

1.4k

Views

Elementary proof that finite sums of square roots of primes is irrational

Published on 03 Apr 2026 - 18:18

score 135 · Answer 6 · 2015-11-16 16:21:13

135

Views

Proof strategy about a property of triangular matrices

Published on 16 Nov 2015 - 16:21

score 222 · Answer 7 · 2026-03-30 02:07:48

222

Views

A new approach to find value of $x^2+\frac{1}{x^2}$

Published on 30 Mar 2026 - 2:07

score 2.2k · Answer 8 · 2015-11-23 00:38:45

2.2k

Views

Proving that $ \chi(G) = \omega(G) $ if $ \bar{G} $ is bipartite.

Published on 23 Nov 2015 - 0:38

score 333 · Answer 9 · 2015-11-23 11:28:52

333

Views

Circular argument in proof?

Published on 23 Nov 2015 - 11:28

score 54 · Answer 10 · 2026-04-03 08:21:56

54

Views

How would you write formal definition for indeterminate limit?

Published on 03 Apr 2026 - 8:21

score 2.4k · Answer 11 · 2015-11-25 18:40:05

2.4k

Views

$X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$

Published on 25 Nov 2015 - 18:40

score 962 · Answer 12 · 2026-03-30 23:57:11

962

Views

Non-integral-over-a-point proof that the probability of any point in a continuous distribution is zero

Published on 30 Mar 2026 - 23:57

score 109 · Answer 13 · 2015-12-01 00:45:57

109

Views

Is there a proof for area theorem, which does not use area argument?

Published on 01 Dec 2015 - 0:45

score 114 · Answer 14 · 2015-12-05 16:31:42

114

Views

Is it possible to prove by contradiction that the boundary of a set in a metric space is closed using these definitions.

Published on 05 Dec 2015 - 16:31

score 133 · Answer 15 · 2015-12-06 02:13:18

133

Views

Show that $\lim\limits_{x\rightarrow 0}f(x)=1$

Published on 06 Dec 2015 - 2:13

List Question

Prove that for any polynomial $P(x)= a_nx^n + \cdots +a_1x+a_0,P$ is differentiable

Is $H$ the Commutator Subgroup of $G$ if $H\neq \{1\}, H\leq G$ and $[H, G] = [H, H]$?

Every function $f:\mathbb{N}\rightarrow\mathbb{R}$ is continuous (using definition)

Prove $ \forall x >0, \quad \sqrt{x +2} - \sqrt{x +1} \neq \sqrt{x +1}-\sqrt{x}$

Elementary proof that finite sums of square roots of primes is irrational

Proof strategy about a property of triangular matrices

A new approach to find value of $x^2+\frac{1}{x^2}$

Proving that $ \chi(G) = \omega(G) $ if $ \bar{G} $ is bipartite.

Circular argument in proof?

How would you write formal definition for indeterminate limit?

$X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$

Non-integral-over-a-point proof that the probability of any point in a continuous distribution is zero

Is there a proof for area theorem, which does not use area argument?

Is it possible to prove by contradiction that the boundary of a set in a metric space is closed using these definitions.

Show that $\lim\limits_{x\rightarrow 0}f(x)=1$

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