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A '''continuous variable''' is a variable such that there are possible values between any two values.
For example, a variable over a non-empty range of the [[real number]]s is continuous
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
In [[statistics|statistical theory]], the [[probability distribution]]s of continuous variables can be expressed in terms of [[probability density function]]s.<ref name="Springer Texts in Statistics">{{cite journal |last1=Dekking |first1=Frederik Michel |last2=Kraaikamp |first2=Cornelis |last3=Lopuhaä |first3=Hendrik Paul |last4=Meester |first4=Ludolf Erwin |date=2005 |title=A Modern Introduction to Probability and Statistics |url=https://doi.org/10.1007/1-84628-168-7 |journal=Springer Texts in Statistics |language=en |doi=10.1007/1-84628-168-7 |isbn=978-1-85233-896-1 |issn=1431-875X|url-access=subscription }}</ref>
In [[continuous time|continuous-time]] [[dynamical system|dynamics]], the variable ''time'' is treated as continuous, and the equation describing the evolution of some variable over time is a [[differential equation]].<ref>{{cite journal |last1=Poyton |first1=A. A. |last2=Varziri |first2=Mohammad Saeed |last3=McAuley |first3=Kimberley B. |last4=MclellanPat James |first4=Pat James |last5=Ramsay |first5=James O. |title=Parameter estimation in continuous-time dynamic models using principal differential analysis |journal=Computers & Chemical Engineering |date=February 15, 2006 |volume=30 |issue=4 |pages=698–708 |doi=10.1016/j.compchemeng.2005.11.008}}</ref> The [[instantaneous rate of change]] is a well-defined concept that takes the ratio of the change in the dependent variable to the independent variable at a specific instant.
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==Discrete variable==
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
Methods of calculus do not readily lend themselves to problems involving discrete variables. Especially in multivariable calculus, many models rely on the assumption of continuity.<ref>{{cite book |last1=Clogg |first1=Clifford C. |last2=Shockey |first2=James W. |title=Handbook of Multivariate Experimental Psychology |date=1988 |publisher=Springer Publishing Company |___location=Boston, Massachusetts |isbn=978-1-4613-0893-5 |pages=337–365}}</ref> Examples of problems involving discrete variables include [[integer programming]].
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