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17 (seventeen) is the natural number ... it is believed that Theodorus had proved all the square roots of non-square integers from 3 to 17 are irrational by ...
A stronger result is the following: [31] Every rational number in the interval ((/) /,) can be written either as a a for some irrational number a or as n n for some natural number n. Similarly, [ 31 ] every positive rational number can be written either as a a a {\displaystyle a^{a^{a}}} for some irrational number a or as n n n {\displaystyle n ...
Irrational numbers ... 11, 13, 17, 19, 23, 29, 31, ... Composite number: A positive integer that can be factored into a product of smaller positive integers. Every ...
Rational numbers have irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem) every irrational number has irrationality exponent at least 2. On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers, including all algebraic irrational numbers , have an irrationality exponent exactly ...
It is assumed that Theodorus had proved that all of the square roots of non-square integers from 3 to 17 are irrational by means of the Spiral of Theodorus. [2] Plato does not attribute the irrationality of the square root of 2 to Theodorus, because it was well known before him. Theodorus and Theaetetus split the rational numbers and irrational ...
In mathematics, an irrational number is any real number that is not a rational number, i.e., ... This page was last edited on 11 December 2022, at 04:17 (UTC).
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A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.