Question

Can the Average of an Infinite Number of Rational Numbers be Irrational?

score 261 · Answer 1 · 2026-02-23 04:41:54

261

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Can the Average of an Infinite Number of Rational Numbers be Irrational?

Published on 23 Feb 2026 - 4:41

score 136 · Answer 2 · 2019-08-08 10:26:01

136

Views

show that if $a,K$ are positive integers and $a≠m^k$ then $a^\frac{1}{K}$ is irrational.

Published on 08 Aug 2019 - 10:26

score 69 · Answer 3 · 2019-08-09 03:28:37

69

Views

Predicting digit sequences in irrational numbers?

Published on 09 Aug 2019 - 3:28

score 149 · Answer 4 · 2026-03-25 20:17:10

149

Views

Is $\log_a b$ irrational for some integer $a$ and algebraic $b$?

Published on 25 Mar 2026 - 20:17

score 49 · Answer 5 · 2026-03-29 04:26:29

49

Views

Can a power series with rational cffs. that sum to irrational lim evaluate to rational lim at non-zero rational point?

Published on 29 Mar 2026 - 4:26

score 68 · Answer 6 · 2019-08-14 17:19:04

68

Views

Some distributions / auto-correlations associated with irrational numbers

Published on 14 Aug 2019 - 17:19

score 1.1k · Answer 7 · 2026-03-29 04:34:45

1.1k

Views

Is even divided by even a rational or irrational number?

Published on 29 Mar 2026 - 4:34

score 53 · Answer 8 · 2026-03-27 20:21:06

Is this : ${\Gamma(1-\alpha)}\int_{0}^\infty \frac{e^{-t}}{{(1+xt)}^{(1-\alpha)}} dt = \int_0^\infty \frac{t^{-\alpha}e^{-t}}{{(1+xt)}} dt$ true?

score 422 · Answer 9 · 2026-03-28 15:12:25

422

Views

Non standard solution to $f(x) = \frac{1}{2}\Big(f(\frac{x}{2}) + f(\frac{1+x}{2})\Big)$

Published on 28 Mar 2026 - 15:12

score 367 · Answer 10 · 2026-03-25 15:24:39

367

Views

Rational approximation of multiple irrationals

Published on 25 Mar 2026 - 15:24

score 100 · Answer 11 · 2026-03-29 07:39:02

100

Views

Constructing a non-empty perfect set of real numbers that does not contain rationals.

Published on 29 Mar 2026 - 7:39

score 353 · Answer 12 · 2019-08-23 10:15:17

353

Views

Irrational inequality. Symbolab and Wolfram Alpha have different answers

Published on 23 Aug 2019 - 10:15

score 211 · Answer 13 · 2019-08-23 15:59:01

211

Views

An elementary way to prove that $\sqrt{2}+\sqrt{3}$ is irrational?

Published on 23 Aug 2019 - 15:59

score 1.8k · Answer 14 · 2019-08-24 01:01:37

1.8k

Views

Can you do modulos with irrational numbers?

Published on 24 Aug 2019 - 1:01

score 78 · Answer 15 · 2026-03-25 17:20:55

78

Views

Re: Construction of a non-empty perfect set of real numbers without rationals

Published on 25 Mar 2026 - 17:20

List Question

Can the Average of an Infinite Number of Rational Numbers be Irrational?

show that if $a,K$ are positive integers and $a≠m^k$ then $a^\frac{1}{K}$ is irrational.

Predicting digit sequences in irrational numbers?

Is $\log_a b$ irrational for some integer $a$ and algebraic $b$?

Can a power series with rational cffs. that sum to irrational lim evaluate to rational lim at non-zero rational point?

Some distributions / auto-correlations associated with irrational numbers

Is even divided by even a rational or irrational number?

Is this : ${\Gamma(1-\alpha)}\int_{0}^\infty \frac{e^{-t}}{{(1+xt)}^{(1-\alpha)}} dt = \int_0^\infty \frac{t^{-\alpha}e^{-t}}{{(1+xt)}} dt$ true?

Non standard solution to $f(x) = \frac{1}{2}\Big(f(\frac{x}{2}) + f(\frac{1+x}{2})\Big)$

Rational approximation of multiple irrationals

Constructing a non-empty perfect set of real numbers that does not contain rationals.

Irrational inequality. Symbolab and Wolfram Alpha have different answers

An elementary way to prove that $\sqrt{2}+\sqrt{3}$ is irrational?

Can you do modulos with irrational numbers?

Re: Construction of a non-empty perfect set of real numbers without rationals

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