Post #1782138
2026-04-27 19:43 UTC
@simon_brooke wrote:
«But it's a fun thought experiment.»
Definitely.
Of course, it's a much bigger endeavor than just working out how to do exponentiation.
I'll only say that the textbooks I have seen give a proof for the particular case of √2 being irrational.
That proof is easy to generalize to the above case.
@screwlisp
Replies (1)
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@simon_brooke@mastodon.scot 2026-04-27 21:47
@vnikolov @screwlisp Aye, I could see root two being irrational. That makes sense. Interestingly, SBCL doesn't think (√2)² = 2: CL-USER[1]: (sqrt 2) 1.4142135 CL-USER[2]: (* (sqrt 2)(sqrt 2)) 1.9999999 I don't know how many bits SBCL's floating point representation is, but that sort of thing is exactly why I don't want to drop to floats when I don't have to.