Real number - Revision history

Lfox: /* Examples */

2024-07-08T18:52:27Z

Examples

← Older revision		Revision as of 18:52, 8 July 2024
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	[[Pi]]		[[Pi]]

	[[e]~~] [TODO I'm not even sure how to define e~~]		[[e]]

	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. [TODO wtf does that mean]		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. [TODO wtf does that mean]

	The Euler-Mascheroni constant (where we don't actually know for sure whether or not it is rational) [TODO I'm not sure if it really makes sense]		The Euler-Mascheroni constant (where we don't actually know for sure whether or not it is rational) [TODO I'm not sure if it really makes sense]

Lfox: /* Examples */

2024-04-22T17:48:23Z

Examples

← Older revision		Revision as of 17:48, 22 April 2024
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	Any [[fraction]].		Any [[fraction]].

	~~Any~~ [[Radical\|algebraic ~~number~~]], like <math>\sqrt{2}</math>.		Some [[Radical\|algebraic numbers]], like <math>\sqrt{2}</math>.

	[[Pi]]		[[Pi]]

	[[e]]		[[e]] [TODO I'm not even sure how to define e]

	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. [TODO wtf does that mean]		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. [TODO wtf does that mean]

	The Euler-Mascheroni constant (where we don't actually know for sure whether or not it is rational) [TODO I'm not sure if it really makes sense]		The Euler-Mascheroni constant (where we don't actually know for sure whether or not it is rational) [TODO I'm not sure if it really makes sense]

Lfox at 17:44, 22 April 2024

2024-04-22T17:44:58Z

← Older revision		Revision as of 17:44, 22 April 2024
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	The concept of real numbers is a ''concept'': it identifies things out in reality. In particular, it does not need to be "constructed" via some set-theoretic method like Dedekind cuts, nor do such constructions even make sense. That any real number can be approximated by fractions is obvious: a fraction is the outcome of directly measuring any quantity with a standard ruler.		The concept of real numbers is a ''concept'': it identifies things out in reality. In particular, it does not need to be "constructed" via some set-theoretic method like Dedekind cuts, nor do such constructions even make sense. That any real number can be approximated by fractions is obvious: a fraction is the outcome of directly measuring any quantity with a standard ruler.

			A real number should really just be the concept of a ''number'', meant in the broadest sense. Strictly speaking, quaternions, complex numbers, elements of finite fields, etc. are not numbers.

	== Examples ==		== Examples ==
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	[[e]]		[[e]]

	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 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. [TODO wtf does that mean]

	The Euler-Mascheroni constant (where we don't actually know for sure whether or not it is rational)		The Euler-Mascheroni constant (where we don't actually know for sure whether or not it is rational) [TODO I'm not sure if it really makes sense]

Lfox at 01:17, 21 April 2024

2024-04-21T01:17:06Z

← Older revision		Revision as of 01:17, 21 April 2024
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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 valid concepts, but the standard definition of the reals involves infinite nonsense.		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.

	~~I don~~'t ''need'' to ~~give them a~~ set-theoretic ~~definition~~. ~~Real numbers are basically just~~ the ~~concept~~ of ~~numbers~~.		The concept of real numbers is a ''concept'': it identifies things out in reality. In particular, it does not need to be "constructed" via some set-theoretic method like Dedekind cuts, nor do such constructions even make sense. That any real number can be approximated by fractions is obvious: a fraction is the outcome of directly measuring any quantity with a standard ruler.

	== Examples ==		== Examples ==

Lfox at 21:35, 18 April 2024

2024-04-18T21:35:56Z

← Older revision		Revision as of 21:35, 18 April 2024
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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 valid concepts, but the standard definition of the reals involves infinite nonsense.		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.

			I don't ''need'' to give them a set-theoretic definition. Real numbers are basically just the concept of numbers.

	== Examples ==		== Examples ==
	Any [[fraction]].		Any [[fraction]].

	Any [[Radical\|algebraic number]] like <math>\sqrt{2}</math>.		Any [[Radical\|algebraic number]], like <math>\sqrt{2}</math>.

	[[Pi]]		[[Pi]]
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	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 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		The Euler-Mascheroni constant (where we don't actually know for sure whether or not it is rational)

Lfox at 20:20, 18 April 2024

2024-04-18T20:20:24Z

← Older revision		Revision as of 20:20, 18 April 2024
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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 ~~real~~, but the standard definition of the reals involves infinite nonsense.		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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	[[e]]		[[e]]

	The ~~output of the following computer program~~		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.

	~~<code>digit(int i): if</code>~~		The Euler-Mascheroni constant

	~~<pre>~~
	~~digit(int i):~~
	~~if (suthaweou)~~
	~~return 0~~
	~~</pre>~~

Lfox: Created page with "I am not yet sure how to define real numbers. Many irrational numbers (e.g.

\sqrt{2}

and

\pi

) are in fact real, but the standard definition of the reals involves infinite nonsense. == Examples == Any fraction. Any algebraic number like

\sqrt{2}

. Pi e The output of the following computer program digit(int i): if

  digit(int i):  if (suthaweou)  return 0

2024-04-18T20:13:08Z

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>"

New page

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 [[Radical|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>