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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Aleph null

Derivation

Properties