Question

How to show that $e$ is irrational by studying $\sum^{n}_{k=1}\frac{1}{k!}$ and $\sum^{n}_{k=0}\frac{1}{k} + \frac{1}{n \cdot n!}$?

score 169 · Answer 1 · 2017-09-16 14:49:31

169

Views

How to show that $e$ is irrational by studying $\sum^{n}_{k=1}\frac{1}{k!}$ and $\sum^{n}_{k=0}\frac{1}{k} + \frac{1}{n \cdot n!}$?

Published on 16 Sep 2017 - 14:49

score 751 · Answer 2 · 2017-09-18 05:25:00

751

Views

Is every real number the supremum of a set of rational numbers?

Published on 18 Sep 2017 - 5:25

score 228 · Answer 3 · 2017-09-18 10:41:34

228

Views

Confusion about $\mathbb Q$ subset suprema?

Published on 18 Sep 2017 - 10:41

score 2.6k · Answer 4 · 2017-09-18 22:24:26

2.6k

Views

Proof technique for between any two real numbers is an irrational number

Published on 18 Sep 2017 - 22:24

score 5.7k · Answer 5 · 2017-09-19 06:58:42

5.7k

Views

How many Irrational numbers?

Published on 19 Sep 2017 - 6:58

score 41 · Answer 6 · 2017-09-20 18:31:19

41

Views

Same amount of irrational numbers in equal size intervals?

Published on 20 Sep 2017 - 18:31

score 131 · Answer 7 · 2017-09-20 20:21:00

131

Views

Is there a method to calculate a dyadic fraction for given irrational number with least error?

Published on 20 Sep 2017 - 20:21

score 807 · Answer 8 · 2017-09-22 09:53:07

807

Views

irrational number: etymology of the word

Published on 22 Sep 2017 - 9:53

score 347 · Answer 9 · 2026-03-25 12:55:24

347

Views

Prove that ${e\over {\pi}}\lt{\sqrt3\over{2}}$ without using a calculator.

Published on 25 Mar 2026 - 12:55

score 848 · Answer 10 · 2017-09-22 19:27:05

848

Views

Proving that $\sqrt{2}$ is irrational with a math level of a middle school student?

Published on 22 Sep 2017 - 19:27

score 1k · Answer 11 · 2026-04-03 14:49:29

1k

Views

Do the multiples of an irrational number modulo 1 cover the unit interval uniformly?

Published on 03 Apr 2026 - 14:49

score 224 · Answer 12 · 2017-09-24 14:33:13

224

Views

An inequality involving irrational numbers

Published on 24 Sep 2017 - 14:33

score 126 · Answer 13 · 2017-09-27 07:27:12

126

Views

How to prove the uncountability of reals by using "describability"?

Published on 27 Sep 2017 - 7:27

score 484 · Answer 14 · 2017-09-27 20:18:47

484

Views

Simplest way of explaining Pi is an irrational number

Published on 27 Sep 2017 - 20:18

score 371 · Answer 15 · 2026-04-05 12:10:07

371

Views

Show that $f(x)$, given by $f(x)=x$ for rational and $f(x)=-x$ for irrational numbers, is continuous at $0$

Published on 05 Apr 2026 - 12:10

List Question

How to show that $e$ is irrational by studying $\sum^{n}_{k=1}\frac{1}{k!}$ and $\sum^{n}_{k=0}\frac{1}{k} + \frac{1}{n \cdot n!}$?

Is every real number the supremum of a set of rational numbers?

Confusion about $\mathbb Q$ subset suprema?

Proof technique for between any two real numbers is an irrational number

How many Irrational numbers?

Same amount of irrational numbers in equal size intervals?

Is there a method to calculate a dyadic fraction for given irrational number with least error?

irrational number: etymology of the word

Prove that ${e\over {\pi}}\lt{\sqrt3\over{2}}$ without using a calculator.

Proving that $\sqrt{2}$ is irrational with a math level of a middle school student?

Do the multiples of an irrational number modulo 1 cover the unit interval uniformly?

An inequality involving irrational numbers

How to prove the uncountability of reals by using "describability"?

Simplest way of explaining Pi is an irrational number

Show that $f(x)$, given by $f(x)=x$ for rational and $f(x)=-x$ for irrational numbers, is continuous at $0$

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