Continuous function and definition

  • Thread starter gummz
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If a function is continuous (nothing else specified), is it defined over R? Continuity means a function's value being the same as the limit for that point IIRC, but I don't know if it being continuous (over R presumably) means that it is also defined over R, or just that it's continuous wherever it is defined.
 

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If a function is continuous (nothing else specified), is it defined over R? Continuity means a function's value being the same as the limit for that point IIRC, but I don't know if it being continuous (over R presumably) means that it is also defined over R, or just that it's continuous wherever it is defined.
If a function is defined as being continuous, with no restrictions, it's probably safe to assume that it is defined for all reals. Sometimes there can be one or more restrictions on the domain that aren't explicitly stated, such as for f(x) = 1/x, whose domain is all nonzero reals.
 

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