# Need Help in Functions (Discrete Math.)

• Jan 31st 2010, 03:36 AM
shehata
Need 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 AM
HallsofIvy
Quote:

Originally Posted by shehata
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 .

Do you know what those words mean? They should be very easy. In fact, any function must fall into one of those categories and so could be used as an example. What about f(n) = 3n? Is it "one-to-one"? Is it "onto"?
• Jan 31st 2010, 06:32 AM
umbrella
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 AM
Plato
Quote:

Originally Posted by umbrella
$\displaystyle f: N \rightarrow N$, 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.

The function $\displaystyle f(x) = 1 / (x - 1)$ is not example.
Because $\displaystyle f: N \not\rightarrow N$.
Do you see why?
• Jan 31st 2010, 09:28 AM
shehata
i didn't understand any thing
i just want an example of function for every question
• Jan 31st 2010, 09:36 AM
Plato
Quote:

Originally Posted by shehata
i didn't understand any thing
i just want an example of function for every question

Those statement do not answer Halls' question.
What are the definition of those types of functions.
If you cannot answer that question then you would be able to understand examples.
• Jan 31st 2010, 12:09 PM
umbrella
I understand why, my bad. It does not map N to N, but instead it maps N to Q. Thank you....