Thread: Neither one-to-one nor onto

Q:Give an explicit formula for a function from the set of all integers to
the set of positive integers that is neither one-to-one nor onto.



Can someone give me some hints as to how I should approach this question because honestly, I have no idea how to do this question.
Answer with explanation would be nice. xD


Thanks,
Creative

Originally Posted by Creative

Q:Give an explicit formula for a function from the set of all integers to
the set of positive integers that is neither one-to-one nor onto.



Can someone give me some hints as to how I should approach this question because honestly, I have no idea how to do this question.
Answer with explanation would be nice. xD


Thanks,
Creative

partition the integers somehow, like even and odd. then just map to one partition. let two integers go to the same integer as well. that will prevent it from being one to one. one of many ways to do this is to use a piece-wise function, or some sort of polynomial

If we let two integers to be on the same partition(even or odd) -not one-one
then how do we get it to be not onto as well?

*edit
so if the function is ((x^2)-8x+7)
x = 7 and x = 1(both in odd partition)
How would you prove it not to be onto?


Thanks,
Creative

Originally Posted by Creative

Q:Give an explicit formula for a function from the set of all integers to the set of positive integers that is neither one-to-one nor onto.

works well and is simple.

How would i explain that?

Originally Posted by Creative

How would i explain that?

Is that function one-to-one? Explain!
Is that function onto? Explain!