Infinity is not a number until you qualify it with a specific set. Aleph Numbers‎ > ‎ Aleph-0. Aleph-null definition is - the number of elements in the set of all integers which is the smallest transfinite cardinal number. Final Project Report. is equinumerous with its initial ordinal), and thus the initial ordinals of the aleph numbers serve as a class of representatives for all possible infinite cardinal numbers. The symbol is known as "aleph-null" rather than "aleph-zero". ZFC set theory, which includes the axiom of choice, implies that every infinite set has an aleph number as its cardinality (i.e. You have to be more specific. [math]\aleph_0[/math] is the smallest cardinal infinity, so we are probably talking in terms of ZFC-set theory. Isn't that the cardinality of algebraic numbers, which IIRC are countable? However, there are some evidence against this thought. It is also called "aleph-naught and "aleph-nought." But it is called "Aleph Null" when you mean the cardinality of the number. Infinity means endless, but Trans-Infinity is bigger than Infinity!?. 1 / infinity = 0. Aleph null * (aleph null - 1) * (aleph null - 2) This does not make sense, as it is infinite. Sitemap. PowerPoint: Degrees of Infinity. It is also known as Aleph-Null. The symbol refers to a set that has the same cardinal number as the “small” infinite set of integers. If you are going to talk about the Aleph numbers, [math]\aleph_{\alpha}[/math], which are transfinite Cardinal numbers, you really ought to know better than to refer to anything as non-specific as “infinity” and the symbol [math]\infty[/math]. So basically (aleph null) aleph null. I think that infinity and aleph null equals zero.

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