Quick question about surjective functions

[jaejoon89]

Question Details:
f(a/b) = 2^a * 3^b where (a/b) is in lowest terms.

Show f is surjective (onto).

Note: f maps positive integers to natural numbers


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Is it sufficient to say that...

It is onto because for every natural number y there is (a/b) s.t. f(x) = y.

 

[rasmhop]

I think you have misunderstood the question.
f(a/b) suggests that f maps from rational numbers and not positive integers. If it mapped from positive integers we would have b=1 always. However even then f isn't surjective. Can you find an a/b in lowest terms such that 2^a * 3^b = 5?

It is onto because for every natural number y there is (a/b) s.t. f(x) = y.

No. Here you just state the definition of a surjective function. You never show that y actually exists.

Perhaps you're really supposed to show it's injective as a function from the rational numbers to the natural numbers?