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Full Idea
The symbol 'aleph-nought' denotes the cardinal number of the set of natural numbers. The symbol 'aleph-one' denotes the next larger cardinal number. 'Aleph-omega' denotes the omega-th cardinal number.
Clarification
'omega' is ω (can't do alephs!). Aleph comes from the Hebrew alphabet
Gist of Idea
'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal
Source
Shaughan Lavine (Understanding the Infinite [1994], III.3)
Book Ref
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.50
15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |