Paradox

I am getting into paradoxes and my mind is becoming unsettled.
We are all familiar with the paradoxes of Zeno that show that contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.
However I have recently stumbled on a series of paradoxes that had previously escaped me. I shall only disclose one at this point because one is enough to seriously damage your brain cells.

The total number of integers (whole numbers 1, 2, 3, 4, 5, .....to infinity) is the same as the total number of "even integers" (whole numbers 2, 4, 6, 8, 10 ....to infinity).
I could provide the proof of this but better to allow you to try to get your head around the concept.

As a 'bonus puzzler' I assume that most of you are already familiar with the concept of a sheet of paper that has only one side. i.e It would be impossible to color one side red and the other side blue because there is only one side.

If you are at all curious as to the 'proof' of either or both of these paradoxes let me know.