Real number: Difference between revisions
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(Created page with "I am not yet sure how to define real numbers. Many irrational numbers (e.g. <math>\sqrt{2}</math> and <math>\pi</math>) are in fact real, but the standard definition of the reals involves infinite nonsense. == Examples == Any fraction. Any algebraic number like <math>\sqrt{2}</math>. Pi e The output of the following computer program <code>digit(int i): if</code> <pre> digit(int i): if (suthaweou) return 0 </pre>") |
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I am not yet sure how to define real numbers. Many irrational numbers (e.g. <math>\sqrt{2}</math> and <math>\pi</math>) are in fact | I am not yet sure how to define real numbers. Many irrational numbers (e.g. <math>\sqrt{2}</math> and <math>\pi</math>) are in fact valid concepts, but the standard definition of the reals involves infinite nonsense. | ||
== Examples == | == Examples == | ||
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The | The number <math>0.x_1 x_2 x_3 x_4 \cdots</math>, where <math>x_i : \{0,1\}</math> is its <math>i</math>th digit in base 2, and where <math>x_i = 1</math> if <math>i</math> is prime, and 0 otherwise. | ||
The Euler-Mascheroni constant | |||
Revision as of 20:20, 18 April 2024
I am not yet sure how to define real numbers. Many irrational numbers (e.g. and ) are in fact valid concepts, but the standard definition of the reals involves infinite nonsense.
Examples
Any fraction.
Any algebraic number like .
The number , where is its th digit in base 2, and where if is prime, and 0 otherwise.
The Euler-Mascheroni constant