Let $(a,b)$ and $(c,d)$ be intervals in $\Bbb R$, and find an injective and surjective function from $(a,b)$ to $(c,d)$

Question

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?

score 7 · Accepted Answer · answered Apr 20 '13 at 12:54

7

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

answered Apr 20 '13 at 12:54

Git Gud

31,356

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

score 4 · Answer 2 · answered Apr 20 '13 at 12:50

4

Hint

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

answered Apr 20 '13 at 12:50

azimut

22,696

Let $(a,b)$ and $(c,d)$ be intervals in $\Bbb R$, and find an injective and surjective function from $(a,b)$ to $(c,d)$

2 Answers2

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