Question

do 1 and 0.99999999... really represent the same number?

Answer 1

yes.

Answer 2

Not really But are close enough for calculation purpose.

Answer 3

depends on what level of math you're at???

Answer 4

yes. here's the proof:

0.999... = 0.9 + 0.09 + 0.009 + ...

this is a geometric series with first term 0.9 and common ratio 0.1, which converges to 0.9/(1 - 0.1) = 1

Answer 5

which are the levels?

Answer 6

@santistebanc: well James just gave the higher and ultimately correct level. but try explaining that to a little kid.

Answer 7

if A = 0.99999...

then A = 0.9 + 0.09 + 0.009 + 0.0009 + ...

then 0.1A = 0.09 + 0.009 + 0.0009 + ...

thus A - 0.1A = (0.9 + 0.09 + 0.009 + 0.0009 + ...) - (0.09 + 0.009 + 0.0009 + ...)

thus 0.9A = 0.9

thus A = 1

Answer 8

I'm a little kid but thanks to everyone, now I get it.

Answer 9

another way to prove it is like this
x = .9999999999...
10x = 9.99999999... (Multiply both sides by 10)
(Now subtract x from each side)
10x-x = 9x
9.9999999... - .99999999... = 9

9x = 9 (Divide by 9)
x = 1

Answer 10

0.33333.....(= 1/3) * 3 = 0.9999...(1).

Answer 11

Gosh, thought we should have at least 100 posts by now:-)