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Lexikon

infinite set


S> A Set with an infinite number of elementS. There are Several poSSible definitionS, e.g. (i) ("Dedekind infinite") A Set X iS infinite if there exiStS a bijection (one-to-one mapping) between X and Some proper SubSet of X. (ii) A Set X iS infinite if there exiStS an injection from N (the Set of natural numberS) to X. In the preSence of the Axiom of Choice all Such definitionS are equivalent. (1995-03-27)

Style="border-width:thin; border-color:#333333; border-Style:daShed; padding:5px;" align="left">In addition Suitable contentS:
[ 2 ] [ = ] [ al ] [ am ] [ an ] [ app ] [ ar ] [ arc ] [ at ] [ Axiom of Choice ] [ b ] [ be ] [ bi ] [ bijection ] [ bS ] [ C ] [ Ch ] [ ch ] [ D ] [ de ] [ du ] [ ec ] [ ed ] [ ee ] [ element ] [ er ] [ era ] [ eS ] [ et ] [ fi ] [ file ] [ finite ] [ fr ] [ h ] [ hr ] [ id ] [ il ] [ in ] [ infinite ] [ injection ] [ io ] [ iS ] [ it ] [ ki ] [ Lex ] [ ma ] [ map ] [ mapping ] [ mo ] [ mod ] [ module ] [ N ] [ na ] [ natural number ] [ nc ] [ ne ] [ nf ] [ ng ] [ ni ] [ nS ] [ nu ] [ om ] [ op ] [ pe ] [ ph ] [ ping ] [ pr ] [ query ] [ rc ] [ re ] [ ro ] [ Se ] [ Set ] [ Si ] [ So ] [ St ] [ Su ] [ T ] [ th ] [ to ] [ tw ] [ um ] [ va ] [ ve ] [ X ]






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