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== | ||
Latest revision as of 19:49, 26 October 2007
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)
for any constant 
.
for any constant 
. (this is debatable with negative numbers)
for any constant 
