User:Peter Schmitt/Notes: Difference between revisions
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imported>Peter Schmitt (Context cardinality) |
imported>Peter Schmitt (two more) |
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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 16:30, 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)
- Ordinal number [r]: The generalization of natural numbers (as means to order sets by size) to infinite sets. [e]
- Infinity [r]: Add brief definition or description
- 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]