Aleph null
From AoPSWiki
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 constant 
.
for any constant 
. (this is debatable with negative numbers)
for any constant . (this is debatable with negative numbers)
