.999~ = 1?

[linksdeity]

Okay, here's the problem at hand...

.999 repeating, is not 1.

if it was 1, than it would be 1.

It goes on, for infinitey, coming ever closer to 1. Sadly, it just isn't 1, so why do people consider it to be 1... which it isn't?

 

[ProviaFan]

http://mathforum.org/dr.math/faq/faq.0.9999.html

 

[BrownTown]

.9999 repeating is 1, exactly 1, not jsut really clsoe, but exactly equal to 1. There are bunches of proofs of this statement.

Heres just 1 of 100:

x=.999999....
10x=9.99999....
10x-x=9.99999-x
9x=9
x=1

or:

1/9 = .111111....
2/9 = .222222....
8/9 = .888888....
9/9 = .999999... = 1

or:

sum from x= 1 to infinity of .9^.1x in this equation a= .9, and r = .1

sum of an infinite series = a/(1-r) = .9/(1-.1) = .9/.9 = 1

 

[CTho9305]

This has been argued repeatedly, and it always boils down to two groups of people:
A) people who know math
B) people who don't

Group A says "yes", and group B says "no". You're welcome to define some other mathematical system in which they're not equal, but it's going to be useless by and large for most tasks we use the normal math systems on.