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I am in a Discrete Structures class, and am stuck on a concept. I am trying to show an example of a function N → N that is neither onto nor one-to-one.

If I use f(x) = 1, this is not onto because the target does not equal the range. My textbook uses the formula if f(a1) = f(a2), then a1 = a2. How would I use this formula in this case to prove my example is correct? (or incorrect?)

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    $f(1)=1$ and $f(2)=1$ but $1\neq 2$, thus your $f$ is not 1-1. – 2017-02-10
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    Read the definition of onto and one-to-one functions carefully. Write it out in words and try to construct small numerical examples for each. Then try to construct a function which is neither onto nor one-to-one. – 2017-02-10
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    Wow, @ThibautDumont , I can't believe I didn't see that.Thanks. – 2017-02-10
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    Those things need a little time to get used to :) – 2017-02-10

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