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we dont need that the smallr the better Tag: Reverted |
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{{Probability fundamentals}}
In contrast, a variable is a '''discrete variable''' if and only if there exists a one-to-one correspondence between this variable and a subset of <math>\mathbb{N}</math>, the set of [[natural numbers]].<ref>{{cite book |last1=Odifreddi |first1=Piergiorgio |title=Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers |date=February 18, 1992 |publisher=North Holland Publishing Company |isbn=978-0444894830 |page=18}}</ref> In other words, a discrete variable over a particular interval of real values is one for which, for any value in the range that the variable is permitted to take on, there is a positive minimum distance to the nearest other permissible value. The value of a discrete variable can be obtained by counting, and the number of permitted values is either finite or [[countably infinite]]. Common examples are variables that must be [[integer]]s, non-negative integers, positive integers, or only the integers 0 and 1.<ref>{{cite book |last1=van Douwen |first1=Eric |title=Handbook of Set-Theoretic Topology |date=1984 |publisher=Elsevier |___location=North Holland |isbn=978-0-444-86580-9 |pages=113–167}}</ref>
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