Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.

I've looked at a few examples on here of how cardinality works and I'm still struggling. This is the problem that I'm currently struggling with. I know there needs to be a bijection function. I'm just stuck on how to actually do it.

• Hint: try a map in the for $g(x)=ax+b$. – user228113 Nov 23 '15 at 4:22
• Hint: What's the equation of a line that goes from $(0,4)$ to $(1,10)$? – John Douma Nov 23 '15 at 4:22
• y=(9/4)x +1 is what the equation should be – Todd Benjamin Nov 23 '15 at 4:25
• @Todd Bejamin: No. $y = \frac{9}{4} x + 1$ runs through $(0, 1)$ and $(4, 10)$, not the points indicated by John Douma. – Daniel R. Collins Nov 23 '15 at 4:35
• Then what Egor said, y= 4 + 6x – Todd Benjamin Nov 23 '15 at 4:44

We need some monotonic function with domain $(0;1)$ and support $(4;10)$, it will definitely be bijection. Obvious candidate is $y = 4 + 6x$, make sure you can find another ones.