Let 25Z be the set of all integers that are multiples of 25. Prove that 25Z has the same cardinality as 2Z, the set of all even integers.
has the same cardinality as ,
where and 2Z is the set of all even integers.
A function is said to be one-to-one function if distinct elements in domain must be mapped with distinct elements in co-domain.
A function is onto function if each element in co-domain is mapped with at least one element in domain.
Now in order to show that have the same cardinality, define a bijective map from .
So, consider the map from defined by, .
Show that is one to one. For this take and consider
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