[split] 0.999... equals 1

[Violet]

Endless, therefore the zeros match every nine you add to the number, and follow that up with a one. It is ENDLESSLY not equal to one.

[Tiberius]

Yes, and so do you not realise the absurdity of the concept of taking an endless amount of 9s and putting a 1 on the end.

I'll repeat the words again:

endless
end

[Eilonnwy]

If it's endless, then it by definition CANNOT be followed up with a 1, because it's fucking endless. You add a 1 at the end and guess what, you just ended it.

We are not talking about 0.9, 0.99, 0.999

We are talking about .9999 repeating for ever and ever, or as it is symbolicly shown:

What part of, "this is an established mathematical fact" are you not getting?

[Violet]

Yes, Adrian... we get the concept I think. The concept is to attach an additional 0 every single time you raise a nine. The .1 was the start with .9, and no matter how far you go back with the nines (Infinitely, you never end the nines), the 0's will match every digit of nines you put in your equation, and still have that 1 following all of them.

Simple: you must add a .repetitive0-1 to make your .9repetitive equal to one. You are infinitely adding 9's, but you will never reach one, no matter how many 9s you add. Add them to kingdom come and you still don't have one. That is the point... you will be infinitely getting CLOSER to one... but you will NEVER reach it.

This can be represented by a very simple graph, I'll show you it when I find it. It curves ever closer to the line of one, but it never hits it.

---

Mathematically, your formula looks like this: O.9(infinite) + 0.0(infinite)1 = 1.

[Rhizomorph13]

A graph that demonstrates the .999... never hits 1 over an infinite range? You will need an infinite amount of paper and an infinite amount of ink. I will see you in an infinite amount of seconds in my infinitly large room where an infinite number of monkeys are working on producing a screenplay of Jack Black's "Tenacious D and the Pick of Destiny" They might accidently produce a copy of all our great literature but I will have to get back to you in an infinite amount of years.

Rhizo

[Retorth]

How about this:

About infinity:
http://en.wikipedia.org/wiki/Hilbert%27s...rand_Hotel

[Rhizomorph13]

Nice site Retorth!

Rhizo

[Retorth]

Nice site Retorth!

Rhizo

Cheers!

It has some really interesting examples and explanations.

[leo-rcc]

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.

Infinity - Infinity is 0.

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

Okay I stand corrected on that one, however .999 to infinity - .888 to infinity does not equal zero though both are infinite.

[Eilonnwy]

Okay I stand corrected on that one, however .999 to infinity - .888 to infinity does not equal zero though both are infinite.

Uh. sure it doesn't, because those aren't the same numbers. o.O

The way I understand it is through fractions. To me it's just another way of expressing 1 through symbols, like how 2/2 = 1

It also helps to think of the fraction 1/3 to better understand. We all know 3/3 = 1

1/3 = .333...
1/3 + 1/3 = .333... + .333...
2/3 = .666...
2/3 +1/3 = .666... + .333...
3/3 = .999...
3/3 = 1 therefore .999 = 1

Does that make it clearer?