regardless of how many 9's there are in that post, that's not even CLOSE to an infinite number of 9's.
I haven't watched the video, but there are a couple of simple ways to show that 0.999... is exactly 1. The simplest relise on the fact that multiplication and division are inverse operations. If I divide by 2, then multiply by 2, i get back my original number. That is a fundamental property of multiplcation.
so, i can take a number...Say 1, and divide it by 3, then multiply that result by three, and i'm back to my original number.
1 / 3 = 0.33333....and on and on forever.
0.3333...and on and on forever * 3 is 0.9999....and on and on forever. And so it must equal 1.
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
posted 1 year ago
Jesper de Jong wrote:. . . (infinitely repeating 9's) is equal to 1. . . . an approximation with a finite number of 9's. . . .
Yes, that is the problem. It should be possible to show that all finite sequences of multiple 9s after the decimal point do not equal 1.0.
1: 0.999999999999999999 = 1.0 (Assumption)
2: 0.9999999999999999999 is closer to 1.0 ∴ 0.9999999999999999999 = 1.0