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The point is that we can represent sqrt(2) symbolically (as I just did there) but it cannot be represented as a binary (or decimal) expansion. Computers can al
by rocqua 8y ago
The point is that we can represent sqrt(2) symbolically (as I just did there) but it cannot be represented as a binary (or decimal) expansion.
Computers can also work symbolically rather than based on some direct binary representation. I think equality and especially comparison become more difficult to determine, but it remains possible.
- vidarh 8y agoBut this merely a product of the choice of representation. Here is a fully expanded representation: 1. Of course my choice of base is a bit exotic, but the point is that no matter what, we're working on symbols. We're just used to seeing some as more direct analogues of numbers than others.
- daveFNbuck 8y agoWhat's a direct binary representation? If that means having each digit explicitly written out, no model of computation could possibly do that in finite time. If it means having the ability to output arbitrary bits in finite time, Turing machines can do that.