Queston is :

Give an example Of afunction From N to N that

1. One to one but not onto.

2.onto but not one to one .

3.Both onto and one to one (but not the identity func.)

4.Nither one to one nor onto .

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- Jan 31st 2010, 03:36 AMshehataNeed Help in Functions (Discrete Math.)Queston is :

Give an example Of afunction From N to N that

1. One to one but not onto.

2.onto but not one to one .

3.Both onto and one to one (but not the identity func.)

4.Nither one to one nor onto .

- Jan 31st 2010, 05:45 AMHallsofIvy
- Jan 31st 2010, 06:32 AMumbrella
Hey I know this one:

one to one is an injective function, onto is a surjective function.

So let's see the first problem:

$\displaystyle f: N \rightarrow N$, so we need a function that does not repeat itself, $\displaystyle f(a) = f(a')$ so $\displaystyle a = a'$. $\displaystyle f(x) = 1 / (x - 1) $ would be sufficient.

As that function does not repeat itself and it has no value for $\displaystyle x = 1$. - Jan 31st 2010, 06:43 AMPlato
- Jan 31st 2010, 09:28 AMshehata
i didn't understand any thing

i just want an example of function for every question - Jan 31st 2010, 09:36 AMPlato
- Jan 31st 2010, 12:09 PMumbrella
I understand why, my bad. It does not map N to N, but instead it maps N to Q. Thank you....