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>. | + | *<math>\aleph_{0}\pm c=\aleph_{0}</math> for any real constant <math>c</math>. |
− | + | *<math>\aleph_{0}\cdot c=\aleph_{0}</math> for any positive real constant. | |
− | *<math>\aleph_{0}\cdot c=\aleph_{0}</math> for any constant | ||
[[Category:Constants]] | [[Category:Constants]] | ||
+ | {{stub}} |
Latest revision as of 17:39, 11 December 2024
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 real constant .
- for any positive real constant.
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