[JadeNB]

> It is easy to map all natural numbers between 0 and 1 on the real line. Just not 1 to 1.

For the usual meaning of the term, you certainly can construct a 1-to-1 (that is, injective) map N \to [0, 1] (for example, n \mapsto 10^(-n)); the natural numbers just can't be mapped onto [0, 1] (that is, the map can't be surjective). That's the opposite of the problem we have: it's saying you can losslessly encode a countable amount of information in an uncountable amount of space; but I'm saying conversely that you can't perform an uncountable number of steps in a countably infinite amount of time.

[pino999]

But the computation steps are certainly countable, even if there are infinite. The amount of steps in time we can take is uncountable. We can always find a point between two other times.Time dilation does exactly this, making the time a computational step take smaller and smaller.