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So here is this question I got stuck on:

Let $(a,b)$, $(c,d)$ be intervals (not sure if that's the correct term) on $\Bbb R$, so that $a<b$, $c<d$. Find an injective and surjective function $f:(a,b)\rightarrow(c,d)$.

Thanks in advance!

P.S. I get these question a lot. Is that some way of thinking, or some general method I should follow to make these question easier for me to solve?

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Interval is correct. – Git Gud Apr 20 '13 at 12:57
up vote 3 down vote accepted

enter image description here

Edit: It's not supposed to be a square.

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I see. Thank you for your constant help! – ohad Apr 20 '13 at 13:02
Congratulations for the 5k! And wow, I have exactly the same score right now. – azimut Apr 20 '13 at 13:03
@ohad No problem. – Git Gud Apr 20 '13 at 13:03
@azimut Thank you and congrats :) – Git Gud Apr 20 '13 at 13:04


Try a function of the form $x \mapsto sx + t$ with $s,t\in\mathbb R$.

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