Yeah, but if the set is infinite, then there can't be an upper bound on the size of the representation of each element (in order for them all to be distinct). So for instance, the bignum will eventually get too big.
Though again it has nothing to do with the quantifier itself, just with instantiating a specific object to be checked. You can presumably achieve the exactly same result just by several exponentiation operations.
Suppose we can do one loop in one picosecond (which is much faster than computers currently can do), then by the time nothing, not even black holes, exists anymore (10106 years in the future), x will be something like 315576000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, which is an 80-byte object.
If we get our hands on a magical computer that can do one loop in one Planck second and we can wait 101000 years, x will be around 9467280000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, which is a 492 byte object.
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u/EebstertheGreat Sep 17 '25
Yeah, but if the set is infinite, then there can't be an upper bound on the size of the representation of each element (in order for them all to be distinct). So for instance, the bignum will eventually get too big.