Jan 6
Number Systems
The reals are weird. Really weird.
From r/mathjokes, by u/Dependent-Pudding-31.
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Number Systems
The reals are weird. Really weird.
From r/mathjokes, by u/Dependent-Pudding-31.
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mathematicians when theyre invited to a function: oh real?
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Just found out about another set of number: algebraic periods, a countable ring between the algebraics and the complex which includes many popular transcendental numbers.
Oh yeah, periods are lurking in the background of a lot of my PhD research but I never wound up focusing on them.
The big thing there is, you can add in any finite (or, I think, countable) set of transcendental numbers and still stay in a countable set. So just "what about pi?" isn't a good explanation of why the reals; you could use the algebraic numbers plus pi (and e), or whatever.
Which is why I focused, not really on the existence of pi, but on the sort of argument that produces it. If you stick to a countable set you could have pi, but you won't be able to make that sort of limiting argument reliably.
Maybe the real numbers are the limits we converged to along the way