#real numbers

[mathhombre]

Number Systems

The reals are weird. Really weird.

From r/mathjokes, by u/Dependent-Pudding-31.

[math-memes]

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[polaroidblog]

“Memoria polaroid” – un blog alla radio S25E34

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[jadagul]

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.

[noelements-setempty]

Maybe the real numbers are the limits we converged to along the way

[lefuette]

Incorrect ntwewy quotes by me #10

Fret: Whenever you "prove" something, you always just throw theorems and mathematical expressions at us that noone understands. All you do is proofs by confusion!

Minamimoto: WHAT DID YOU JUST SAY?!

Fret: You heard me! I bet you can't do those "proofs" from scratch!

Minamimoto: *sighs*

Minamimoto: Alright, should we start with an axiomatic definition of the real numbers or construct them?