[split] 0.999... equals 1

[Rob]

Wolfram Alpha is not performing the correct calculation.
when you ask it to multiply 0.999 by 10 the value it comes up with is 9.990

in order to feed it the correct starting value of X I have given it (1/3)*3. it returns 9, as expected:
http://www.wolframalpha.com/input/?i=10X...1%2F3%29*3

Its quite likely that its rounding up at some stage, as this is a computer system and they have finite space to hold and compute infinity recursive numbers.

[Meatball]

It makes sense, but it's hard for some people to wrap their heads around.

You have to think of it as an assertion that's neccesary for math not to implode.

The simplest way I can think of it is how 1/9 = .111..., therefore 9/9 = .999... = 1.

Inifinty is a crazy thing.

[Retorth]

Indeed it is trippy.

[Eilonnwy]

I'm confused that people are actually arguing this point? This is an established mathematical truth. There are concepts in mathematics that fly in the face of common sense. It's actually kind of neat.

[Tiberius]

Here is another way of explaining it. Each number is different from another by a specific amount. 2 is 1 different from 1, 1.5 is 0.5 different from 1.

However there is no gap between 0.999 (with an infinite number of 9's) and 1. If there were, then you wouldn't have an infinite number of 9's. Ergo, 0.999... and 1 are the same number.

No, it is 9X, 10X-1X. If you are going to multiply infinite numbers then the outcome is infinite as well. Subtraction of an infinite value will give you another infinite value.

.999... (to infinity) - .999... (to infinity) will always equal zero, because it is the same value.

If you think you've disproved this, then you could probably win some mathematical prize, given that 0.999.... = 1 is accepted as mathematical truth.

Or you are suffering from one of these common fallacies which usually cause students of mathematics to reject the concept: http://en.wikipedia.org/wiki/0.999...#Sk..._education

[Violet]

The gap is infinite 0, ending in a one.

[Meatball]

Is that a joke?

[Tiberius]

Unfortunately I don't think it is. It seems not many people here have grasped mathematics involving infinities

[Violet]

It is not a joke.

0.9 < 1 by .1
0.99 < 1 by .01
0.999 < 1 by .001
This continues infinitely. No matter how many nines you add... it will always be less than one. Infinite .9999 < 1 by Infinite 0.0000 with a one occurring at the end.

[Tiberius]

You do realise what the word "infinite" means don't you?