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## Homework Statement

Give an explicit formula for a function f : ℕ ⇒ ℕ that is

a) onto, but not one-to-one.

b) neither one-to-one nor onto.

**1. The attempt at a solution**

a) The formula f[itex]_{2}[/itex](n)= ⌊[itex]\frac{n}{3}[/itex]⌋. it's onto cause f[itex]_{2}[/itex](3n)= n for every n. but, it's not one-to-one, cause f[itex]_{2}[/itex](1)= ⌊[itex]\frac{1}{3}[/itex]⌋ = 0 = f[itex]_{2}[/itex](0)

b) f[itex]_{4}[/itex](n)=4 ⌊[itex]\frac{n}{4}[/itex]⌋. This is not one-to-one, cause it's counterexample f[itex]_{4}[/itex](0) = f(1) = 0. Nor is it onto cause there is no odd number in the range of f[itex]_{4}[/itex]

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