persian52
- 13
- 0
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_{2}(n)= ⌊\frac{n}{3}⌋. it's onto cause f_{2}(3n)= n for every n. but, it's not one-to-one, cause f_{2}(1)= ⌊\frac{1}{3}⌋ = 0 = f_{2}(0)
b) f_{4}(n)=4 ⌊\frac{n}{4}⌋. This is not one-to-one, cause it's counterexample f_{4}(0) = f(1) = 0. Nor is it onto cause there is no odd number in the range of f_{4}
Last edited: