Difference between revisions of "Aleph null"

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==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>.
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*<math>\aleph_{0}\pm c=\aleph_{0}</math> for any real constant <math>c</math>.
*<math>\aleph_{0}/c=\aleph_{0}</math> for any constant <math>c\ne 0</math>. (this is debatable with negative numbers)
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*<math>\aleph_{0}\cdot c=\aleph_{0}</math> for any positive real constant.
*<math>\aleph_{0}\cdot c=\aleph_{0}</math> for any constant <math>c\ne 0</math>. (this is debatable with negative numbers)
 
  
 
[[Category:Constants]]
 
[[Category:Constants]]
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Latest revision as of 17:39, 11 December 2024

Aleph null ($\aleph_{0}$) is the infinite quantity with the least magnitude. It generally is regarded as a constant of ring theory.

Derivation

$\aleph_{0}$ 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 ($\aleph_{1}$), which is the second smallest infinite quantity.

Properties

$\aleph_{0}$ has several properties:

  • $\aleph_{0}\pm c=\aleph_{0}$ for any real constant $c$.
  • $\aleph_{0}\cdot c=\aleph_{0}$ for any positive real constant.

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