Aleph null

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 constant $c$.
  • $\aleph_{0}/c=\aleph_{0}$ for any constant $c\ne 0$. (this is debatable with negative numbers)
  • $\aleph_{0}\cdot c=\aleph_{0}$ for any constant $c\ne 0$. (this is debatable with negative numbers)
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