Comment by donkeybeer
3 days ago
Yes but like I was thinking more how you'd do any kind of "and it vanishes" or even "becomes sufficiently small" with a gappy number system as it would have to pass through gaps where "undefined" non-rationals exist.
3 days ago
Yes but like I was thinking more how you'd do any kind of "and it vanishes" or even "becomes sufficiently small" with a gappy number system as it would have to pass through gaps where "undefined" non-rationals exist.
I guess my stance (which is not very well-developed or anything) is that you try to learn to live with the gaps: define everything in terms of only what you can measure and it no longer matters whether a number is rational or irrational, or infinitesimal vs small-but-finite, because you can't tell. Instead of saying "it vanishes" as an absolute statement you say "it appears to vanish from my perspective".