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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
by philipov 4y ago
>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'.
- LittlePeter 4y agoThat is a nice insight.
- kgwgk 4y agoWe could even say that within any range we are interested in there are infinitely many of them.
- visarga 4y agoA single real number can contain all the information ever produced by humanity.
- LordDragonfang 4y agoSimilarly put, the infinite number of reals is also a bigger infinity than the infinite number of integers (aleph-null).