Difference between revisions of "Aleph null"
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| − | '''Aleph null''' (<math>\aleph_{0}</math>) is the [[infinity|infinite]] quantity with the least magnitude. It generally is regarded as a [[constant]] of [[ring theory]] | + | '''Aleph null''' (<math>\aleph_{0}</math>) is the [[infinity|infinite]] quantity with the least magnitude. It generally is regarded as a [[constant]] of [[ring theory]]. |
==Derivation== | ==Derivation== | ||
| Line 6: | Line 6: | ||
==Properties== | ==Properties== | ||
<math>\aleph_{0}</math> has several properties: | <math>\aleph_{0}</math> has several properties: | ||
| − | *<math>\aleph_{0}\pm c=\aleph_{0}</math> for any constant <math>c</math>. | + | *<math>\aleph_{0}\pm c=\aleph_{0}</math> for any real constant <math>c</math>. |
| − | + | *<math>\aleph_{0}\cdot c=\aleph_{0}</math> for any positive real constant. | |
| − | *<math>\aleph_{0}\cdot c=\aleph_{0}</math> for any constant | ||
[[Category:Constants]] | [[Category:Constants]] | ||
| − | + | {{stub}} | |
Latest revision as of 18:39, 11 December 2024
Aleph null (
) is the infinite quantity with the least magnitude. It generally is regarded as a constant of ring theory.
Derivation
can be expressed as the number of terms in any arithmetic sequence, geometric sequence, or harmonic sequence. It is less than, for example, aleph 1 (
), which is the second smallest infinite quantity.
Properties
has several properties:
for any real constant 
.
for any positive real constant.
for any real constant 
.
for any positive real constant.This article is a stub. Help us out by expanding it.
