Is there a way to prove equivalent cardinalites?

[Hodgey8806]

Homework Statement

I'm just a bit stupefied at trying to prove a cardinality. I'm not sure I have the skills, but I would like to show that the cardinalities of R (the real numbers) and the interval on (0,1) are equivalent.--to be clear, the interval here is all real numbers between (0,1).

Homework Equations

I suppose I could show some sort of bijection between the two, but I don't know how to begin it. I do realize that I will need a more general definition than an actual formula.

The Attempt at a Solution

I'm stuck here. I don't know how to begin exactly. This is not my homework problem. In fact, my homework is to show that the cardinalities of R and the interval of real numbers (1,infinity) are equivalent.

Any tips would be very appreciated!

 

[Deveno]

one thing that occurs to me is that if you suitably restricted the domain of the tangent function, you'd map an interval symmetric around 0 to all of R.

then it's just a matter of tinkering around with the argument of the tan function to keep it within (0,1).

finally, you want to show that this gives you a bijection of (0,1) with R, which is equivalent to showing the inverse function exists.