1 = 0.999999999999999999999999999999... ?

>ignore 2/3 of post
Then you're calling out my laziness. I don't give a fuck. I've made my point, and a shitty non-technical definition from google was sufficient. Fuck off pedantic brainlet.

[point]
: an end or object to be achieved : purpose

>contradicting exactly nothing

[kon-truh-dikt]
to assert the contrary or opposite of; deny directly and categorically.

[bait]
food used to entice fish or other animals as prey.

Why are you bringing in physics? The number line is truly continuous such that for EVERY pair of distinct real numbers there exists a third number between them. As a matter of fact, there exist infinitely many distinct real numbers between them.

>oh he's being an idiot just like I was
>he must be baiting
right over your head, fucking brainlet

Since you appear to be genuinely stupid, my copypasta definition was meant to highlight incorrect usage of said word. Please fuck off, child.

By definition for every real number there exists a sequence of numbers converging against it, and if a sequence of rational numbers converges it converges against a real number.
Showing that 0.999... converges against 1 is trivial therefore we dont need this thread every week.

Let n = 0.99999999999999....
Suppose (for contradiction) n > 1.

Then consider 1 - n.

Since 1 > n, 1 - n > 0.

Yet there is no positive number m, with n > m > 0. Thus n is the smallest positive number. This violates the Archimedes property.