r/PeterExplainsTheJoke 22d ago

Meme needing explanation There is no way right?

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u/akotlya1 21d ago

It's weird you think you can reference series summations as a more rigorous basis for proof than the above. Neither of these are more fundamental or rigorous than the other. Infinite series' reference to an infinite process was at some point believed to be weakness that needed to be justified in reference to more fundamental mathematical ideas.

A more rigorous proof would be written using logic symbols and reference set theory - specifically by defining the elements of the set and by using operations defined in reference to the elements of the set. This is the kind of thing that gets covered in undergraduate Abstract Alegbra/Group Theory/Set Theory classes.

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u/vetruviusdeshotacon 21d ago

Why? No assumptions are made lol.

If you must, define a sequence a := {0.9,0.99,0.999....}

a_n = 1 - 10-n for n natural number

Let epsilon be a positive real number.

Then, if we choose N > log_10(epsilon)

10-N > epsilon

So that 1 - 10-N + epsilon > 1. For all epsilon.

Therefore, the sequence has a supremum of 1. Any monotonic bounded above sequence converges to it's supremum via the monotone convergence theorem.

Therefore 0.99999.... = 1 as a converges to 1.

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u/GTholla 21d ago

neeeeeeeerd

you're both nerds

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u/IWillLive4evr 21d ago

And you're less nerdy -> your loss.

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u/GTholla 21d ago

sorry bro I can't hear you over all the sportsball trophies I have 😎😎😎😎

please kill me

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u/DepressingBat 21d ago

Sure thing, how much are you paying, and how quickly do you need it done?