>>10427804

But you forgot the remainder.

Consider

a)10/3 = 3+R1

b)100/3 = 33+R1

c)1000/3 = 333+R1

d)10000/3 = 3333+R1

e)100000/3 = 33333+R1

Oh wait there's that pesky remainder you keep forgetting about. It's negligible in many everyday computations, that's why the math works so well above and beyond. Not to mention random noise outright discards this noise. But you know darn right that remainder will be there even in an infinite sequence. Maybe it is clear now, or maybe you are still skeptical but 1/3 will yield a remainder now matter how far you go because 10/3 will never be equal to 3 evenly. That is a mathematical fact so basic that higher levels can only forget about it when it becomes infinitely small(not 0).

So as you can probably see now, 0333... != R1+0.3333.....; these are two different numbers not a way to write

>>bbbbut, since 0.333... is infinite you will never get to add back in the remainder. That is true. But what is also true, is that this can be rewritten as a finitely long number: 0.333(10/3) and likewise this number can be written as 0.3333(10/3) = 0.33333(10/3)=0.333333333333333333(10/3).

It should not be hard to see that if I multiply this number by 3, the result is identically 1.