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Cantor diagonal argument; related number

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Prove that if $x$ and $y$ are irrational numbers, there exists an irrational number $z$ such that $y < z < x$

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How do I check if intervals can be nested?

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Prove $\alpha \in\mathbb R$ is irrational, when $\cos(\alpha \pi) = \frac{1}{3}$

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What type of numbers are roots of $x^{2} = -1$ themselves?

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square root of 2 irrational - alternative proof

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Yet another product of irrational numbers

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#elementary-number-theory #arithmetic #irrational-numbers
85
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Is this irrationality proof correct?

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#proof-verification #irrational-numbers #alternative-proof
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Are there any number systems better suited to nature?

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Represent non-integer values on the factorial base

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#irrational-numbers #number-systems #transcendental-numbers
98
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Calculate digits of $\pi$ without needing to reuse them

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379
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Periodicity with irrational numbers

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#calculus #number-theory #irrational-numbers
105
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How to know equation solution irrational

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Are there any general results about the irrationality of $a^{\frac{p}{q}}$?

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#reference-request #irrational-numbers
186
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Periodicity with irrational numbers

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