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Show that the function f: N → N: f(x) = x2 is one-one and into.

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We know that

f (x1) = f (x2)

So we get

x12 = x22

It can be written as

(x1 – x2) (x1 + x2) = 0

We get

x1 – x2 = 0 where x1 = x2

Hence, f is one one.

Consider 2 is the co-domain of N where √2 ∉ N

f (√2) = (√2)2 = 2

Hence, f is into.

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