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I'm trying to find an example of a continuously differentiable function from $\mathbb{R}$ to $\mathbb{R}$ that is injective but not surjective.

I can easily find one from $\mathbb{Z}$ to $\mathbb{Z}$ but I'm having difficulty finding one for the reals.

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What's the one you have for the Integers? –  JB King Mar 5 '13 at 0:11

1 Answer 1

Hint: It might be easier than expected.

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+2 for cleverness in delivery! Okay, I guess I can't do that. Well, +1, anyway. –  Cameron Buie Mar 4 '13 at 21:02
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He wanted a function, not a punction ;) –  Hagen von Eitzen Mar 4 '13 at 21:24
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@HagenvonEitzen This thread's only big enough for one pun master--so you can just git out. –  Alex Youcis Mar 4 '13 at 21:31
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Punny, we are all so punny here. –  JB King Mar 4 '13 at 23:15
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@AlexanderGruber: Yeah, it's strange. My guess is that the **...** notation for bold was invalidated because the closing ** was followed immediately by letters, whereas the inner *...* notation for italics did not have that issue. To work around this in a question or an answer (but not in a comment), one can use the HTML-style notation: easier than <b>exp</b>ected. –  ruakh Mar 4 '13 at 23:41

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