Search results
Results from the WOW.Com Content Network
A bijective function, f: X → Y, from set X to set Y demonstrates that the sets have the same cardinality, in this case equal to the cardinal number 4. Aleph-null, the smallest infinite cardinal. In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set.
The continuum hypothesis says that =, i.e. is the smallest cardinal number bigger than , i.e. there is no set whose cardinality is strictly between that of the integers and that of the real numbers. The continuum hypothesis is independent of ZFC , a standard axiomatization of set theory; that is, it is impossible to prove the continuum ...
The following even stronger large cardinal properties are not consistent with the axiom of choice, but their existence has not yet been refuted in ZF alone (that is, without use of the axiom of choice). weakly Reinhardt cardinal, Reinhardt cardinal, Berkeley cardinal, super Reinhardt cardinal, totally Reinhardt cardinal
In the other direction, the binary expansions of numbers in the half-open interval [,), viewed as sets of positions where the expansion is one, almost give a one-to-one mapping from subsets of a countable set (the set of positions in the expansions) to real numbers, but it fails to be one-to-one for numbers with terminating binary expansions ...
In linguistics, and more precisely in traditional grammar, a cardinal numeral (or cardinal number word) is a part of speech used to count. Examples in English are the words one , two , three , and the compounds three hundred [and] forty-two and nine hundred [and] sixty .
Main page; Contents; Current events; Random article; About Wikipedia; Contact us
aleph-nought, aleph-zero, or aleph-null) is the cardinality of the set of all natural numbers, and is an infinite cardinal.The set of all finite ordinals, called or (where is the lowercase Greek letter omega), also has cardinality .
In the mathematical discipline of set theory, a cardinal characteristic of the continuum is an infinite cardinal number that may consistently lie strictly between (the cardinality of the set of natural numbers), and the cardinality of the continuum, that is, the cardinality of the set of all real numbers. The latter cardinal is denoted or .