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A '''continuous variable''' is a variable whose value is obtained by measuring, i.e., one which can take on an [[uncountable set]] of values.
For example, a variable over a non-empty range of the [[real number]]s is continuous, if it can take on any value in that range. The reason is that any range of real numbers between <math>a</math> and <math>b</math> with <math>a, b \in \mathbb{R}; a \neq b</math> is uncountable, with infinitely many values within the range.<ref>{{cite journal |last1=Brzychczy |first1=Stanisaw |last2=Gorniewicz |first2=Lech |title=Continuous and discrete models of neural systems in infinite-dimensional abstract spaces |journal=Neurocomputing |date=2011 |volume=74 |issue=17 |page=2711-2715 |doi=10.1016/j.neucom.2010.11.005}}</ref>
Methods of [[calculus]] are often used in problems in which the variables are continuous, for example in continuous [[optimization]] problems.<ref>{{Cite book |last1=Griva |first1=Igor |url=https://www.worldcat.org/oclc/236082842 |title=Linear and nonlinear optimization |last2=Nash |first2=Stephen |last3=Sofer |first3=Ariela|author3-link= Ariela Sofer |publisher=Society for Industrial and Applied Mathematics |year=2009 |isbn=978-0-89871-661-0 |edition=2nd |___location=Philadelphia |pages=7 |language=en |oclc=236082842}}</ref>
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