User:Peter Schmitt/Notes: Difference between revisions
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{{r|zero (mathematics)}} [[0]] [[0 (number)]] [[zero]] [[zero (disambiguation)]] | {{r|zero (mathematics)}} [[0]] [[0 (number)]] [[zero]] [[zero (disambiguation)]] | ||
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{{r|Neighbourhood (topology)}} | |||
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:: {{r|clopen||}} | |||
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Revision as of 11:15, 2 October 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]
- Countable [r]: In mathematics, a property of sets — see: Countable set (A set with as many elements as there are natural numbers, or less.) [e]
- Uncountable [r]: In mathematics, a property of sets — see: Countable set (A set with as many elements as there are natural numbers, or less.) [e]
- Uncountable set [r]: A set with more elements than there are natural numbers. (See: Countable set.) [e]
- 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]
- 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
- Infinite set [r]: The number of its elements is larger than any natural number. (See: Finite set.) [e]
- Finite set [r]: The number of its elements is a natural number (0,1,2,3,...) [e]
- Finite and infinite [r]: The distinction between bounded and unbounded in size (number of elements, length, area, etc.) [e]
- 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]
- Continuum hypothesis [r]: A statement about the size of the continuum, i.e., the number of elements in the set of real numbers. [e]
- Zero (mathematics) [r]: The number of elements in an empty set, and a digit or symbol. [e] 0 0 (number) zero zero (disambiguation)
- Neighbourhood (topology) [r]: In a topological space, a set containing a given point in its interior, expressing the idea of points "near" this point. [e]
- Boundary point [r]: (of a set) In geometry and topology, a point such that every neighbourhood contains both points in the set and points not in the set. [e]
- Clopen [r]: In topology, a combination of closed and open (clopen set). [e]
- Clopen set [r]: In topology, a set with empty boundary which therefore is both closed and open. [e]
- Open set [r]: In geometry and topology, a set that does not contain any of its boundary points. [e]
- Closed set [r]: In geometry and topology, a set that contains its boundary; the complement of an open set. [e]