Let D be the set of all set of all finite subsets of positive integers, and define by the following rule: For every integer the set of all of the positive divisors of n.
Whether is one-to-one or not.
Consider be the set of all finite subsets of positive integers, and is defined by the rule: For all integers the set of all of the positive divisors of .
In one-to-one function, distinct elements in domain are mapped with distinct elements in co-domain.
Claim: is a one-to-one function.
For this consider . Without loss of generality assume that
Whether is onto or not.
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