When.com Web Search

Search results

  1. Results From The WOW.Com Content Network
  2. Cardinality - Wikipedia

    en.wikipedia.org/wiki/Cardinality

    There are two ways to define the "cardinality of a set": The cardinality of a set A is defined as its equivalence class under equinumerosity. A representative set is designated for each equivalence class. The most common choice is the initial ordinal in that class. This is usually taken as the definition of cardinal number in axiomatic set theory.

  3. Cardinal number - Wikipedia

    en.wikipedia.org/wiki/Cardinal_number

    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.

  4. Cardinality of the continuum - Wikipedia

    en.wikipedia.org/wiki/Cardinality_of_the_continuum

    The set of real algebraic numbers is countably infinite (assign to each formula its Gödel number.) So the cardinality of the real algebraic numbers is . Furthermore, the real algebraic numbers and the real transcendental numbers are disjoint sets whose union is .

  5. Cantor's theorem - Wikipedia

    en.wikipedia.org/wiki/Cantor's_theorem

    As a consequence, the cardinality of the real numbers, which is the same as that of the power set of the integers, is strictly larger than the cardinality of the integers; see Cardinality of the continuum for details.

  6. Continuum (set theory) - Wikipedia

    en.wikipedia.org/wiki/Continuum_(set_theory)

    The cardinality of the continuum is the size of the set of real numbers. The continuum hypothesis is sometimes stated by saying that no cardinality lies between that of the continuum and that of the natural numbers , ℵ 0 {\displaystyle \aleph _{0}} , or alternatively, that c = ℵ 1 {\displaystyle {\mathfrak {c}}=\aleph _{1}} .

  7. Cardinal characteristic of the continuum - Wikipedia

    en.wikipedia.org/wiki/Cardinal_characteristic_of...

    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 .

  8. Scott's trick - Wikipedia

    en.wikipedia.org/wiki/Scott's_trick

    Thus one may define the representative of the cardinal number of to be the set of all sets of rank that have the same cardinality as . This definition assigns a representative to every cardinal number even when not every set can be well-ordered (an assumption equivalent to the axiom of choice).

  9. Set (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Set_(mathematics)

    A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...