0.9 Repeating is Equal to 1

9.9(repeating) = 10x
0.9(repeating) = 1x
Subtracting gives you 9 = 9x, or 1=x.

This seems odd because we think the real numbers are repre-
sented by decimals in some exact fashion, when in fact that is not true at
all (this is the most obvious manifestation). Figuring out exactly what
real numbers were took an awfully long time for mathematicians of previous
centuries. One way to think about this particular problem is, 0.9 = 9/10,
0.99 = 99/100 etc., and so what is the number you might expect to get as you
continue that sequence? Mathematically, the limiting value cannot be
anything other than 1, because there is no real number smaller than 1 which
does not eventually also become smaller than one of these fractions
99 . . . 9/100 . . . 0

Edit:

Wrong forum, please move this.

Moved to General Conversation.

9.9(repeating) = 10x 0.9(repeating) = 1x Subtracting gives you 9 = 9x, or 1=x. This seems odd because we think the real numbers are repre- sented by decimals in some exact fashion, when in fact that is not true at all (this is the most obvious manifestation). Figuring out exactly what real numbers were took an awfully long time for mathematicians of previous centuries. One way to think about this particular problem is, 0.9 = 9/10, 0.99 = 99/100 etc., and so what is the number you might expect to get as you continue that sequence? Mathematically, the limiting value cannot be anything other than 1, because there is no real number smaller than 1 which does not eventually also become smaller than one of these fractions 99 . . . 9/100 . . . 0 Edit:   Wrong forum, please move this.

Why do we need to know this? ahh math is gay!

9.9(repeating)=9.9(repeating)

Plain and simple.

.9 repeating = .1 repeating *9

.1 repeating=1/9

1/9 *9=9/9

9/9=1

All it is is limits... Nothing more advanced than high school calculus.

This is the oldest, stupidest math proof ever. Actually depending on what type of way you look at it, both answers can be proved, undeniably.

not if "x" is going towards positive "+" infinity or negative "-" infinity then you are talking about multiple variables which is caliculus bc (which i failed in math class in college) will be continued.....

Moved to General Conversation.

Basically .9 repeating is infinitely close to 1 without actually being 1.