Word domain can have several meanings in mathematics. Probably the most often used meaning is the one referring to domain of function (or map in general). In that sense domain of function `f:X to Y` is set `X` of all values for which function `f` is defined.
Another important term regarding domain of a function is natural domain. Natural domain is maximal set of values for which the function can be defined under real numbers. E.g. for...
Word domain can have several meanings in mathematics. Probably the most often used meaning is the one referring to domain of function (or map in general). In that sense domain of function `f:X to Y` is set `X` of all values for which function `f` is defined.
Another important term regarding domain of a function is natural domain. Natural domain is maximal set of values for which the function can be defined under real numbers. E.g. for function `f(x)=x^2` natural domain is set of all real numbers `RR` (because we can square every real number and we will get a real number), while for function `g(x)=\sqrt(x)` natural domain is set of all non-negative real numbers (if we take square root of a negative number, we get an imaginary number).
Word domain is also used in topology to denote a connected open set.
In number theory integral domain is ring that is commutative under multiplication, has multiplicative identity and no divisors of zero. Example of integral domain are integers.
In control theory and statistics frequency domain refers to function analysis with respect to frequency. E.g. each sound signal can be broken down to several different simple signals of different frequencies. Frequency domain is set of those simple signals.
There are still other usages of the word domain in mathematics: fundamental domain in group theory, domain of discourse in logic... There even a whole branch of mathematics called domain theory that studies partially ordered sets which are sometimes called domains.
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