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When someone says a real valued function $f(x)$ on $\mathbb{R}$ is finite, does it mean that $|f(x)| \leq M$ for all $x \in \mathbb{R}$ with some $M$ independent of $x$?

  • 15
    What you are describing is what is usually called a *bounded* function. I have not seen the English word *finite* used in this context. Perhaps you could mention the context in which the term was used.2012-05-17
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    As we can see from the contradictory answers (I would choose George's answer), the OP must provide some context to get something useful.2013-02-10
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    Just pointing out that "finite" sometimes also means nonzero (with a finite measure, usually $>0$). In the sense that $dx$ can be understood as infinitesimal, but still finite interval. Most likely not in this case, but if we are discussing semantics, we should include all the cases.2015-08-07
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    For example $x\mapsto \frac{1}{x}$ is finite valued on $]0,\infty [$ since for all $x\in ]0,\infty [$, $-\infty , but it's not valued on $[0,\infty [$ since $f(0)=+\infty $.2015-10-05
  • 0
    Possible duplicate of : [What does 'finite-valued' mean?](http://math.stackexchange.com/questions/710573/what-does-finite-valued-mean)2016-08-27

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