Question

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

score 262 · Answer 1 · 2026-04-09 08:09:32

262

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

Published on 09 Apr 2026 - 8:09

score 139 · Answer 2 · 2026-04-15 23:58:49

139

Views

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

Published on 15 Apr 2026 - 23:58

score 72 · Answer 3 · 2026-04-11 05:03:26

72

Views

Predicting digit sequences in irrational numbers?

Published on 11 Apr 2026 - 5:03

score 150 · Answer 4 · 2026-05-11 03:50:34

150

Views

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

Published on 11 May 2026 - 3:50

score 53 · Answer 5 · 2026-04-17 11:45:20

53

Views

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

Published on 17 Apr 2026 - 11:45

score 71 · Answer 6 · 2026-04-14 14:18:12

71

Views

Some distributions / auto-correlations associated with irrational numbers

Published on 14 Apr 2026 - 14:18

score 1.1k · Answer 7 · 2026-04-15 11:34:20

1.1k

Views

Is even divided by even a rational or irrational number?

Published on 15 Apr 2026 - 11:34

score 55 · Answer 8 · 2026-04-15 17:21:23

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 424 · Answer 9 · 2026-04-16 00:11:20

424

Views

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

Published on 16 Apr 2026 - 0:11

score 368 · Answer 10 · 2026-05-10 17:58:13

368

Views

Rational approximation of multiple irrationals

Published on 10 May 2026 - 17:58

score 102 · Answer 11 · 2026-04-15 07:47:05

102

Views

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

Published on 15 Apr 2026 - 7:47

score 356 · Answer 12 · 2026-04-15 01:33:45

356

Views

Irrational inequality. Symbolab and Wolfram Alpha have different answers

Published on 15 Apr 2026 - 1:33

score 214 · Answer 13 · 2026-04-13 17:11:11

214

Views

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

Published on 13 Apr 2026 - 17:11

score 1.8k · Answer 14 · 2026-04-08 18:46:49

1.8k

Views

Can you do modulos with irrational numbers?

Published on 08 Apr 2026 - 18:46

score 80 · Answer 15 · 2026-04-15 18:21:37

80

Views

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

Published on 15 Apr 2026 - 18:21

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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