Question

Does $0\prec B \prec A$ imply $A^{-1}B \prec I$

score 89 · Answer 1 · 2026-04-11 17:27:34

89

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Does $0\prec B \prec A$ imply $A^{-1}B \prec I$

Published on 11 Apr 2026 - 17:27

score 3.2k · Answer 2 · 2026-03-25 09:50:06

3.2k

Views

Suppose a and b are real numbers. Prove that if $a < b < 0$ then $a^2 > b^2$

Published on 25 Mar 2026 - 9:50

score 278 · Answer 3 · 2018-12-01 12:16:55

278

Views

Inequality proof $\frac{x}{y}+2\frac{y}{z}+3\frac{z}{x} \geq 3\sqrt[3]{6} $

Published on 01 Dec 2018 - 12:16

score 203 · Answer 4 · 2026-04-09 15:45:44

203

Views

How to find an appropriate constant value to which the function will be defined

Published on 09 Apr 2026 - 15:45

score 81 · Answer 5 · 2018-12-01 18:56:05

81

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Values of $x$ satisfying $\sin x\cdot\cos^3 x>\sin^3x\cdot\cos x$

Published on 01 Dec 2018 - 18:56

score 86 · Answer 6 · 2018-12-01 19:18:18

86

Views

For all $x \in \Bbb R$, if $x > 4$ then $x^2 > 9$

Published on 01 Dec 2018 - 19:18

score 148 · Answer 7 · 2026-03-26 01:34:33

148

Views

For every real number $x$, $ \lvert 2x - 6 \rvert \gt x \iff \lvert x-4 \rvert \gt 2 $

Published on 26 Mar 2026 - 1:34

score 75 · Answer 8 · 2018-12-01 22:09:47

75

Views

If $|a-1|<\epsilon$ and $|a-2|<\epsilon$ prove that $\epsilon>1/2$

Published on 01 Dec 2018 - 22:09

score 177 · Answer 9 · 2026-03-27 08:42:56

177

Views

Find all non-negative integers $a, b$ satisfying $|4a^2 - b^{b+1}| \leq 3$

Published on 27 Mar 2026 - 8:42

score 53 · Answer 10 · 2018-12-02 08:43:55

53

Views

Show that $\lvert\frac{1}{x} \sin x-\sum _{k=0}^n (-1)^k\frac{x^{2k}}{(2k+1)!}\rvert\leq\frac{|x|^{2n+1}}{(2n+2)!}$

Published on 02 Dec 2018 - 8:43

score 97 · Answer 11 · 2026-04-03 15:43:19

97

Views

Proving $f$ zero function if $|f'(x)|\le A|f(x)|$

Published on 03 Apr 2026 - 15:43

score 83 · Answer 12 · 2018-12-02 15:22:19

83

Views

Prove that $2\sqrt{\frac{a}{a+c}}-\frac{9\sqrt{c^2+1}}{8c}<1$ with $a;c>0$

Published on 02 Dec 2018 - 15:22

score 73 · Answer 13 · 2026-04-12 22:34:04

73

Views

Can we prove this inequality holds for some region?

Published on 12 Apr 2026 - 22:34

score 190 · Answer 14 · 2026-04-10 13:42:53

190

Views

Smallest integer power for an inequality to hold

Published on 10 Apr 2026 - 13:42

score 40 · Answer 15 · 2026-03-26 01:29:18

40

Views

Let $a,b,c,d\in\Bbb{R}$ such that $|c|\ne|d|$. Prove that $\frac{a+b}{c+d}\le\frac{|a|+|b|}{||c|-|d||}$

Published on 26 Mar 2026 - 1:29

List Question

Does $0\prec B \prec A$ imply $A^{-1}B \prec I$

Suppose a and b are real numbers. Prove that if $a < b < 0$ then $a^2 > b^2$

Inequality proof $\frac{x}{y}+2\frac{y}{z}+3\frac{z}{x} \geq 3\sqrt[3]{6} $

How to find an appropriate constant value to which the function will be defined

Values of $x$ satisfying $\sin x\cdot\cos^3 x>\sin^3x\cdot\cos x$

For all $x \in \Bbb R$, if $x > 4$ then $x^2 > 9$

For every real number $x$, $ \lvert 2x - 6 \rvert \gt x \iff \lvert x-4 \rvert \gt 2 $

If $|a-1|<\epsilon$ and $|a-2|<\epsilon$ prove that $\epsilon>1/2$

Find all non-negative integers $a, b$ satisfying $|4a^2 - b^{b+1}| \leq 3$

Show that $\lvert\frac{1}{x} \sin x-\sum _{k=0}^n (-1)^k\frac{x^{2k}}{(2k+1)!}\rvert\leq\frac{|x|^{2n+1}}{(2n+2)!}$

Proving $f$ zero function if $|f'(x)|\le A|f(x)|$

Prove that $2\sqrt{\frac{a}{a+c}}-\frac{9\sqrt{c^2+1}}{8c}<1$ with $a;c>0$

Can we prove this inequality holds for some region?

Smallest integer power for an inequality to hold

Let $a,b,c,d\in\Bbb{R}$ such that $|c|\ne|d|$. Prove that $\frac{a+b}{c+d}\le\frac{|a|+|b|}{||c|-|d||}$

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