There are as many numbers between 0 and 1, as there are numbers greater than 1!

Examples

2/3 - 3/2, 1/7 - 7/1, 3/4 -4/3, 11/126781 - 126781/11

Find a number greater than 1 whose singlar and only possible multiplicative inverse or reciprocal that is not, greater than 0 but less than 1, and gain immortality.

I have no idea what the question is, or how to answer it; however, in theory the "space" between zero to one should be identical to the space between 1 and 2. Similarly, there would be an infinite number of spaces between each integer pair greater than 2. Therefore, the number of numbers greater than 1 should be greater than the number between 0 and 1, based on so much more (infinite) space.

You're missing the point, m_connors.

If a/b is a real greater than 1 (but less than infinity) b/a will be greater than 0 but less than 1.

For any real a/b

That is the "magic" of it.

What you say about spaces is theoretically true, m_connors. But we must remember that the space between any 2 rationals contains the same number of reals. But the sequence of the multiplicative inverse of any reals greater than 1, only falls under the space of 0 and 1.