Define by the rule: For each integer n, S(n)=the sum of the positive divisors of n.
Whether is one-to-one or not.
A function is defined by the rule:
For all integers the sum of the positive divisors of .
In one-to-one function, distinct elements in domain are mapped with distinct elements in codomain.
Claim: is not one-to-one.
Counter example: let are two integers such that
Whether is onto or not.
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