# Prove the equivalence of [-1,4) ~(2,11) [duplicate]

I need to prove the equivalence of sets [-1,4) ~(2,11) using:

a) Cantor-Bernstein Theorem

b) Constructing a bijection between those two sets.

What I have done:

a) I understand that in-order to prove this using Cantor-Bernstein you need to show injection from $f(x): [-1,4)\rightarrow (2,11)$ and $g(x): (2,11) \rightarrow [-1,4)$

I tried to find corresponding $x$'s so that $f(x)$ would always be in range of $(2,11)$ but I couldn't set up a proper ruleset.

b) Contructing a bijection:

If we have $A =$ {-1, ... 4} We would have to construct a $B =$ {2 +- $rule$ .... 11} The result would be a function $f(x) =$ { a set of rules}.

For example $2-x, x < 0$ and $2 \frac{3}4 * x , x > 0$.

Here also I couldn't understand how do I know to look for these rules, if anyone could provide any insight.

Best regards.

## marked as duplicate by Asaf Karagila♦ elementary-set-theory StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Dec 12 '17 at 17:18

• Hint: For $(a)$, all you need to do is map $[-1,4)$ inside of $(2,11)$, so adding $4$ would be enough. Don't try to make the map surjective. – Michael Burr Dec 9 '17 at 14:11