List questions from irrational-numbers

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Proving f(x)=0 for all x in [a,b] when we only know that f is continuous and f(x)=0 when x is rational.

Published on 11 Dec 2015 - 2:29

313

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Prove that $\sqrt{2} + \sqrt[3]{3}$ is irrational

Published on 12 Dec 2015 - 10:26

3.6k

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Proof: Is there a line in the xy plane that goes through only rational coordinates?

Published on 12 Dec 2015 - 18:50

1.3k

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Are the irrationals as a subspace in the real line and in the plane a connected space?

Published on 13 Dec 2015 - 0:41

102

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Can finite sums of two numbers come arbitrarily close to zero?

Published on 22 Dec 2015 - 9:56

643

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Approximation of $\pi$ using Brahmagupta's Identity

Published on 30 Mar 2026 - 7:07

74

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How is this limit being solved? I can't grasp it

Published on 03 Apr 2026 - 0:29

143

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How to prove $e^{n}$ is irrational?

Published on 24 Dec 2015 - 12:27

287

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Is $\frac{1}{2^{2^{0}}}+\frac{1}{2^{2^{1}}}+\frac{1}{2^{2^{2}}}+\frac{1}{2^{2^{3}}}+....$ algebraic or transcendental?

Published on 28 Mar 2026 - 2:24

829

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$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational

Published on 31 Dec 2015 - 17:05

2.3k

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Why are there more Irrationals than Rationals given the density of $Q$ in $R$?

Published on 04 Jan 2016 - 22:02

322

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Is $\sum_{n \ge 1}{\frac{p_n}{n!}}$ irrational?

Published on 26 Mar 2026 - 22:15

82

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How do I know if this will be rational or irrational? ($a^b$)

Published on 09 Jan 2016 - 15:33

41

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the summation goes to the integration

Published on 09 Jan 2016 - 21:48

3.3k

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How can a Cauchy sequence converge to an irrational number?

Published on 28 Mar 2026 - 2:10

List Question

Proving f(x)=0 for all x in [a,b] when we only know that f is continuous and f(x)=0 when x is rational.

Prove that $\sqrt{2} + \sqrt[3]{3}$ is irrational

Proof: Is there a line in the xy plane that goes through only rational coordinates?

Are the irrationals as a subspace in the real line and in the plane a connected space?

Can finite sums of two numbers come arbitrarily close to zero?

Approximation of $\pi$ using Brahmagupta's Identity

How is this limit being solved? I can't grasp it

How to prove $e^{n}$ is irrational?

Is $\frac{1}{2^{2^{0}}}+\frac{1}{2^{2^{1}}}+\frac{1}{2^{2^{2}}}+\frac{1}{2^{2^{3}}}+....$ algebraic or transcendental?

$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational

Why are there more Irrationals than Rationals given the density of $Q$ in $R$?

Is $\sum_{n \ge 1}{\frac{p_n}{n!}}$ irrational?

How do I know if this will be rational or irrational? ($a^b$)

the summation goes to the integration

How can a Cauchy sequence converge to an irrational number?

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