Function Domain Empty Set

For any set x and any subset s of x the inclusion map s x which sends any element s of s to itself is injective.

Function domain empty set. 1 is it a function. The empty set has no element so x x f x f x is always true. Such a function is then called a partial function.

Y y there exists x x such that f x y. The rationale for this comes from carefully examining the definitionof function in this degenerate. First i was thinking of the chain rule but something looked strange about the function.

In mathematics the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. Definition of surjective is. So according to this definition the answer would be no a function cannot have the empty set as the domain.

If not explain why. 3 is the function one to one. X x f x f x.

2 if yes what are it s domain and range. Since a function is defined on its entire domain its domain coincides with its domain of definition. Definition of injective is.

However this coincidence is no longer true for a partial function. However a function from the reals to the reals does not mean that the domain of the function is the whole set of the real numbers but only that the domain is a set of real numbers that contains a non empty open interval. Sometimes it is useful to consider functionswhose domain is the empty set.