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I am looking for a function which is non $0$ between two $x$ coordinates and $0$ for all other coordinates. I have found one function like this, which is $\frac{1}{x^{\infty}+1}$: see image. However, it is not ideal, as $1^{\infty}$ is indeterminate. Do you know of any other such functions? I have also played around with equations involving square roots, however this doesn't seem to work as then the function is undefined for all values not between the x coordinates, which is something that I don't want.

Image of function

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  • $\begingroup$ What kind of functions are you looking for? It's very trivial if you allow for piecewise functions. (Though $x^\infty$ is hardly a well-defined, good notation.) $\endgroup$ Mar 3 at 5:34
  • $\begingroup$ Yes, @Mather: What is your definition of function? The answer Mike Pierce gave is perfectly fine. $\endgroup$
    – Jo Mo
    Mar 3 at 5:42
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$$f(x) = \begin{cases}1 \text{ if } |x|<1\\0 \text{ otherwise}\end{cases}$$

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    $\begingroup$ Dunno why this is downvoted.... $\endgroup$ Mar 3 at 5:38
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What about smooth bump functions?

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