[split] 0.999... equals 1

[Retorth]

I don't get your calculation...but I do know that you cannot compare this mathematical equation with whole numbers because thats the beauty of this. It is based on "infinity". It's like trying to compare a cat and a dog. They are both animals but they are still different in that one is a cat and the other is a dog. You have to look at it in its respective perspective.

Look at it in this way then:

1/3 = 0.333333333333333333(infinite3) <-- This you can obtain through any standard calculator of course.

2/3 = 0.333333333333333333(infinite3) + 0.333333333333333333333(infinite3)
= 0.666666666666666666(inifinite6)

3/3 = 0.666666666666666666(infinite6) + 0.333333333333333333333(infinite3)
= 0.999999999999999999(infinite9)

Therefore,
3/3 = 0.999999999999999999(infinite9) and 3/3 = 1

so 0.9999999999999999999(infinite9) = 1


Its actually what Eilonwwy showed in an earlier post, so credit to her on this.

I think the reason you don't seem to get it is because you look at it as a finite number of "9"s at the end. If its a finite number then yes this whole thing is inaccurate.

E.g.

If X = 0.99

10X = 9.9

10X - X = 9.9 - 0.99 = 8.91

And this will be the same no matter how many different combinations of 9's you use. However, like what Adrian has been saying, if the number of 9's is infinite, even if you multiply 0.999999999999999(infinite9) by 10 or by 100 for that matter, the number of .999999999(infinite9) never changes because its infinite. It keeps on going.