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Not necessarily. There are series over all kinds of subsets and supersets of the set of real numbers.

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Q: Is a series a function whose domain is the set of real number?
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Is sequence a function?

yes it is a function because sequence defined as "a function whose domain is set of natural number"


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Can anybody answer this hard question Function of x bracket 1 if X is a rational number or 0 if X is an Irrational number?

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What the set of the x values also known as domain?

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