"Suppose there is a mapping from the natural numbers onto the decimals."
Infinity is a tricky subject.
There are infinite naturals, fractions and decimals but they are different kinds of infinities. If we define natural positives as N and both positive and negatives as the same infinities N * 2 (with a minus sign), we can safely say that decimals are simply all naturals multiplied by infinity N * N * N * 2 or N ^ 3 * 2 where for every single integer like 0, 1 or 2 there will be infinite decimals after the point prefixed by infinite zeroes too like .1 .01 .001 .0001 and even if N * 2 or N ^ 3 are equal to infinity (infinity because we can't measure it or at least not know its final boundary) both infinities are different.
Infinity is a tricky subject.
There are infinite naturals, fractions and decimals but they are different kinds of infinities. If we define natural positives as N and both positive and negatives as the same infinities N * 2 (with a minus sign), we can safely say that decimals are simply all naturals multiplied by infinity N * N * N * 2 or N ^ 3 * 2 where for every single integer like 0, 1 or 2 there will be infinite decimals after the point prefixed by infinite zeroes too like .1 .01 .001 .0001 and even if N * 2 or N ^ 3 are equal to infinity (infinity because we can't measure it or at least not know its final boundary) both infinities are different.
And guessable, we're out of hell someday.