This is a stupid question but I am slightly confused about the wording about this.
>Show that if a set S has cardinality m, where m is a positive integer, then there is a one-to-one correspondence between S and the set {1,2,3,...,m}.
By this do they mean that there exists a function such that is a bijection?
Because surely not all functions from S to {1,2,3,...,m} will be bijections because all the domain elements can just map to a single element for example f(x) = 1 for all values of x in S...
Am I understanding this correctly?
>Show that if a set S has cardinality m, where m is a positive integer, then there is a one-to-one correspondence between S and the set {1,2,3,...,m}.
By this do they mean that there exists a function such that is a bijection?
Because surely not all functions from S to {1,2,3,...,m} will be bijections because all the domain elements can just map to a single element for example f(x) = 1 for all values of x in S...
Am I understanding this correctly?
