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>Real numbers can’t be perfectly represented in hardware simply because there are infinitely many of them.

There are also infinitely many integers, but we can represent them just fine inside a finite bound. The problem with reals (and rationals to a lesser extent) is that, within any range we are interested in, a single real number can be infinitely 'long'.




A single real number can contain all the information ever produced by humanity.


Oh, wow! Which one?


I would tell you, but it's too big to fit in the margin.


Similarly put, the infinite number of reals is also a bigger infinity than the infinite number of integers (aleph-null).


We could even say that within any range we are interested in there are infinitely many of them.


That is a nice insight.




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