User:Peter Schmitt/Notes: Difference between revisions

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imported>Peter Schmitt
(Context cardinality)
 
imported>Peter Schmitt
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: {{def|uncountable}}  
: {{def|uncountable}}  
: {{def|uncountable set}}
: {{def|uncountable set}}
{{r|transfinite number}}
{{r|cardinal number}}  
{{r|cardinal number}}  
: {{def|aleph-0}}  
: {{def|aleph-0}}  
: {{def|aleph-1}}
: {{def|aleph-1}}
{{r|ordinal number}}
{{r|infinity}}  
{{r|infinity}}  
: {{def|infinite}}  
: {{def|infinite}}  

Revision as of 17:30, 3 July 2009

  • Cardinality [r]: The size, i.e., the number of elements, of a (possibly infinite) set. [e]
  • Countable set [r]: A set with as many elements as there are natural numbers, or less. [e]
In mathematics, a property of sets — see: Countable set (Template loop detected: Template:Def)
In mathematics, a property of sets — see: Countable set (Template loop detected: Template:Def)
A set with more elements than there are natural numbers. (See: Countable set.)
  • Transfinite number [r]: An infinite number, either a cardinal number or an ordinal number. [e]
  • Cardinal number [r]: The generalization of natural numbers (as means to count the elements of a set) to infinite sets. [e]
Cardinality (size) of the set of all natural numbers.
(Add definition for aleph-1)
Greater in size (number of elements, length, area, etc.) than any natural number
The number of its elements is larger than any natural number. (See: Finite set.)
  • Finite set [r]: The number of its elements is a natural number (0,1,2,3,...) [e]
Bounded (or limited) in size (length, area, etc., or number of elements) by a natural number
  • Hilbert's hotel [r]: A fictional story which illustrates certain properties of infinite sets. [e]
  • Galileo's paradox [r]: The observation that there are fewer perfect squares than natural numbers but also equally many. [e]