Question

Let $n \in \Bbb{N}$. Let $x_1,x_2,\ldots,x_n$ be positive real numbers such that $\prod_{i=1}^n x_i = 1$. Prove that $\sum_{i=1}^n x_i \ge n $

score 116 · Answer 1 · 2018-03-21 20:08:24

116

Views

Let $n \in \Bbb{N}$. Let $x_1,x_2,\ldots,x_n$ be positive real numbers such that $\prod_{i=1}^n x_i = 1$. Prove that $\sum_{i=1}^n x_i \ge n $

Published on 21 Mar 2018 - 20:08

score 69 · Answer 2 · 2026-03-17 20:00:34

69

Views

Are my proofs correct for basic addition properties for natural numbers?

Published on 17 Mar 2026 - 20:00

score 1.6k · Answer 3 · 2026-03-17 07:38:00

1.6k

Views

Cancellation law for multiplication of natural numbers

Published on 17 Mar 2026 - 7:38

score 61 · Answer 4 · 2026-03-17 10:01:12

61

Views

Trying to prove various things about (in)equalities

Published on 17 Mar 2026 - 10:01

score 134 · Answer 5 · 2026-03-17 07:34:09

134

Views

Why isn't $0+a=a$ something we derive?

Published on 17 Mar 2026 - 7:34

score 63 · Answer 6 · 2018-03-29 01:42:13

$f_1$ and $f_2$ map $\omega$ into a set $A$. $f_1(n)=G(f_1 \restriction n) \space \& \space f_2(n)=G(f_2 \restriction n)$. Show $f_1 = f_2$.

score 12k · Answer 7 · 2018-03-29 04:51:59

12k

Views

Is it correct to say that the natural numbers are a proper subset of the integers?

Published on 29 Mar 2018 - 4:51

score 88 · Answer 8 · 2026-03-16 22:46:29

88

Views

$a < b$ iff $S(a) \leq b$

Published on 16 Mar 2026 - 22:46

score 94 · Answer 9 · 2026-03-17 04:36:17

94

Views

Find all natural numbers $n$ for which $n = n'$

Published on 17 Mar 2026 - 4:36

score 60 · Answer 10 · 2018-04-01 19:33:15

60

Views

What is the term for an ordered set/sequence containing natural numbers zero through x inclusive?

Published on 01 Apr 2018 - 19:33

score 91 · Answer 11 · 2026-03-17 20:28:24

91

Views

How to show that $ \langle \sqrt n \rangle $ is not converging

Published on 17 Mar 2026 - 20:28

score 103 · Answer 12 · 2018-04-06 17:55:20

103

Views

A finite axiomatization of $\mathbb N$ and two non-standard models

Published on 06 Apr 2018 - 17:55

score 92 · Answer 13 · 2026-03-17 21:38:21

92

Views

Formula to find square root of a Natural number using only addition and subtraction.

Published on 17 Mar 2026 - 21:38

score 196 · Answer 14 · 2026-03-16 21:13:15

196

Views

Prime Numbers and Infinity

Published on 16 Mar 2026 - 21:13

score 260 · Answer 15 · 2026-03-17 22:38:42

260

Views

Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$

Published on 17 Mar 2026 - 22:38

List Question

Let $n \in \Bbb{N}$. Let $x_1,x_2,\ldots,x_n$ be positive real numbers such that $\prod_{i=1}^n x_i = 1$. Prove that $\sum_{i=1}^n x_i \ge n $

Are my proofs correct for basic addition properties for natural numbers?

Cancellation law for multiplication of natural numbers

Trying to prove various things about (in)equalities

Why isn't $0+a=a$ something we derive?

$f_1$ and $f_2$ map $\omega$ into a set $A$. $f_1(n)=G(f_1 \restriction n) \space \& \space f_2(n)=G(f_2 \restriction n)$. Show $f_1 = f_2$.

Is it correct to say that the natural numbers are a proper subset of the integers?

$a < b$ iff $S(a) \leq b$

Find all natural numbers $n$ for which $n = n'$

What is the term for an ordered set/sequence containing natural numbers zero through x inclusive?

How to show that $ \langle \sqrt n \rangle $ is not converging

A finite axiomatization of $\mathbb N$ and two non-standard models

Formula to find square root of a Natural number using only addition and subtraction.

Prime Numbers and Infinity

Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$

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