You know how much simple math is devoid of the laws of reality?
I mean, you don't
HONESTLY believe that s(t) = a*t^2 + v0*t + s0 (Position function for objects in Free Fall) is ever true in reality, or that F(grav) = g*m1*m2 / d^2 (Newton's Universal Law of Gravitation) holds the far reaches of space together?
Because they don't.
Back on topic, there's a more difficult-to-reject proof to the whole matter. Sure simple algebra can seem to prove, but people can raise objections to specific cases that wouldn't prove to be 100% true - that's probably due to the fact that the variable involved remains ambiguous. But, the algebraic proof is pretty much workable for most of the modern world.
However, if you want to get down and dirty with some of the proofs involved, here's one you can try to figure out.
You know how numbers are composed of right? Ever since ... 1st grade? You've learned that multiple-digit numbers belong to categories like, ones digit, tens digit, hundreds digit, and so on.
Meaning: 2530 is basically 2 * 1000 + 5 * 100 + 3 * 10 + 0 * 1
or 2 * (10^3) + 5 * (10^2) + 3 * (10^1) + 0 * (10^0)
Got that so far right?
So what is 0.75? 0 * (1/10)^0 + 7 * (1/10)^1 + 5 * (1/10)^2
That means...
0.999 is 0 * (1/10)^0 + 9 * (1/10)^1 + 9 * (1/10)^2 + 9 * (1/10)^3
This can be rewritten as an infinite series.
As you apply the generic ideas of (2nd year) calculus, I'm sure you'll be able to easily see how it all simplifies out.
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