>>3
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Anonymous2013-08-31 7:57
Since cardinality is such a common concept in mathematics, a variety of names are in use. Sameness of cardinality is sometimes referred to as equipotence, equipollence, or equinumerosity. It is thus said that two sets with the same cardinality are, respectively, equipotent, equipollent, or equinumerous.
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Anonymous2013-08-31 8:42
* Enumerable: lowest, intermediate, and highest
* Innumerable: nearly innumerable, truly innumerable, and innumerably innumerable
Some programming languages, such as Java[13] and J,[14] allow the programmer an explicit access to the positive and negative infinity values as language constants. These can be used as greatest and least elements, as they compare (respectively) greater than or less than all other values. They are useful as sentinel values in algorithms involving sorting, searching, or windowing.
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Anonymous2013-08-31 10:13
Set theory as a foundation for mathematical analysis, topology, abstract algebra, and discrete mathematics is likewise uncontroversial; mathematicians accept that (in principle) theorems in these areas can be derived from the relevant definitions and the axioms of set theory.
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Anonymous2013-08-31 10:59
One motivation for this use is that a number of generally accepted mathematical results, such as Tychonoff's theorem, require the axiom of choice for their proofs. Contemporary set theorists also study axioms that are not compatible with the axiom of choice, such as the axiom of determinacy.