this post was submitted on 27 Jun 2024
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There's a Real Analysis proof for it and everything.
Basically boils down to
Even simpler: 1 = 3 * 1/3
1/3 =0.333333....
1/3 + 1/3 + 1/3 = 0.99999999... = 1
But you're just restating the premise here. You haven't proven the two are equal.
This step
And this step
Aren't well-defined. You're relying on division short-hand rather than a real proof.
ELI5
Mostly boils down to the pedantry of explaining why 1/3 = 0.(3) and what 0.(3) actually means.
the explanation (not proof tbf) that actually satisfies my brain is that we're dealing with infinite repeating digits here, which is what allows something that on the surface doesn't make sense to actually be true.
Infinite repeating digits produce what is understood as a Limit. And Limits are fundamental to proof-based mathematics, when your goal is to demonstrate an infinite sum or series has a finite total.
That actually makes sense, thank you.