[split] 0.999... equals 1

[Tiberius]

Why are you bringing infinity into it? This is not a discussion of infinity as a value (and I am well aware of the arguments that infinity is not a value...I agree wholeheartedly with them). Infinity is completely different from infinitely long numbers though. An infinitely long number doesn't equal infinity, as it could be 1.999999... (infinitely long string of 9's), making the number equal to 2 (or for sake of your argument, "just less" than 2).

Infinity is a concept tied very much to 1.9^. Infinity is an uncertain value... because of its endless nature. Until you remove the uncertainty from 1.9^... you cannot calculate with certainty. Infinity is not a number (value/whatever), it is a concept... and it is a concept present within 1.9^ that makes the number itself incalculable (because you have a value under the effects of an infinite concept, which makes the number undefined.).

Infinity is not an uncertain value. It isn't a value at all. You contradict yourself several times in this paragraph alone because you refer to infinity as a value and then say it isn't a number/value. Infinity as a value does not work, and the proof of this is easy enough. We aren't using it as a value however, so there isn't any panic.

If one has tied an infinite concept into a value, as one can see with .9^: then one has made the value of this number dependent upon infinity. The value of .9^ is based within something without calculable value. I thought I should bring this up before I disproved this 'equality'.

No it hasn't. The mere fact that we can write .9^ and know precisely what it means disproves your assertion that it isn't calculable. It might take an infinite amount of time to calculate it, but it is still calculable. Long division can show us that quite easily.

An infinitesimal is a number that cannot be measured because it is "so" small. It cannot be distinguished from 0. Your number 0.0^1 is not an infinitesimal number for two reasons:

1) You cannot logically or mathematically have an infinite string of 0's (as denoted by your 0^) which is then followed by a 1. We have been over this. An infinite string has no end, so you have no place to put the 1 on.
2) Even if this number were to exist, it is easily distinguishable from 0, since it is 0.0^1 away from 0. Ergo it does not have the attributes of an infinitesimal number.

An infinitesimal is 'the infinith' number of infinity. By the very definition of it, 0.0^1 is the definition of the infinitesimal. It is no easier to distinguish from 0 than .9^ is from 1. They are an equivalent distance away from 0 and 1. The reason infinitesimals exist is because the infinith number exists. Infinity is like an endless gap... between two pieces of land infinitely far away from each other (And that land exists, just so much as that gap exists). .9^12343 is no different in this concept. If you remove the infinite from the value: you can calculate that 12343. That is why such numbers are able to exist, assuming infinites can be calculated at all.

There is no such thing as the "infinith" number of infinity, mainly because with infinity you can always go one further. I'm going to take a guess at what happened here. You wanted to sound clever without doing much work, so you quickly skim read the Wikipedia article on infinitesimals. You saw the word "infinith" and decided that sounded pretty cool and smart, so you wrote that word down.

Shame you didn't read further, since you would have learned that:

The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.

This is what you get from reading Wikipedia without understanding basic concepts I guess. You contradict yourself again by saying Infinity is both "endless" and that it can have "12343" on the end.

If you don't like Wikipedia, I suggest you don't use it to try and argue about infinitesimals. If you want other sources, I suggest you use Google:

I didn't say that I don't like wikipedia... I said it is not always a reliable source. If mathematicians truly think this, then they are incorrect. So far as I can tell, and I have seen no reason to think otherwise: these 'proofs' are nothing but errors of mathematics.

The Wikipedia page was written by mathematicians...duh! I gave you links before to University mathematics departments on the proof that 0.999... = 1. Take it up with them if you like...but I wouldn't.

This is exactly your error in proving this inequality is equal. You have removed the infinite from the equation. An infinitely long string of numbers is infinite. It is undefinable, and it is endlessly long (thus endlessly gargantuan). Is a hot fire not fire? Then is something infinitely long not infinite? (The Identity's Equality). Not at all. The concept is exactly the same. In 'infinitely long' you are describing the length as being infinite. And here again you are tying an infinite into the definition (and thus value) of something. That's what is being done here .0^1 & .9^

No, an infinitely long string of numbers is not infinite. It is infinitely long (I thought I'd covered that with the original descriptor). Is something infinitely long not infinite? Yes, of course it is. Here is a proof:

0.999... is an infinitely long number
2 (or any number above 1) is greater than it.
Infinity cannot have any numbers greater than it.
Ergo 0.999... is not infinite.
Q . E . fuckin' D.

What you are doing is exactly what you accused me of doing before, taking an infinite and removing it, making it finite. .0^1 as a number cannot exist. You cannot have an infinite number with a finite end.

This is precisely why these 'proofs' fail to prove what they are trying to do: they are removing the infinite from the equation to prove it. That is fallacious reasoning to me. And some people do not believe that one even can remove an infinite.

There was no infinite to begin with. I've been over that.

And thus you are no longer proving that the infinitely long number is equal to a finite number... because you have cancelled out specifically that which you are trying to prove. I do not deny that this is basic math... that it is simple basic math that 1 ≠ .9^ is my point entirely in fact.

Ok, so by that logic if I wanted to prove a fraction was equal to another fraction, canceling out the fraction means the proof is wrong since I've canceled out specifically that which I was trying to prove? Ok, so maths is broken...

1/2 = 2/4

(multiple both sides by 4)

2 = 2

Oh noes! The fractions are gone! 2 =/= 2!

Yeah...erm...bullshit.

Umm... 2.2^x9 = 19.9^8. which is ≠ to 20 (even further from equality than .9^ is from 1). In one of the equations, the infinitely long number remains. In the other: it has been neutralized. This discrepancy between otherwise equivalent methods is because an infinite is an undefined, and until you remove the undefined: you cannot have a defined. In one method it was removed, and the finite answer of 20 is available. In the other: it was not removed, and 19.9^8 is the closest approximate we can get. It remains undefined.

Ok, please get out your calculator and type in 20 / 9. The answer? 2.2^

Now do some basic algebra:

20 / 9 = 2.2^
(multiple both sides by 9)
20 = 2.2^ x 9.

Again, your lovely example had yet more errors, with the number 19.9^8 which doesn't exist, because *takes a deep breath* YOU CAN'T HAVE AN INFINITELY LONG NUMBER WITH A FINITE END...

Citing my gapped land example above: yes, you can. You can have an infinitely long value separating other values. There is no impossibility about it. An infinitesimal is infinitely small number, which can easily be represented by 0.0^1... infinite zeros to show that it is infinitely small... and a 1 for the infinith digit to show that it is different than zero. Once again: nothing impossible about it.

You are indisputably a moron. Instead of reading misreading Wikipedia, please go and ask some Mathematics professor (preferably one who has a PhD) to teach you something correct for a change.

And actually, infinity - infinity would cancel itself out into 0... just as much any other infinite concept. Unless the two infinites are of different length of course, which would make one of them not infinite.

Ok, so apparently you didn't even pass Math at age 15, where I learned the proof that this doesn't work at all. Here it is for your enjoyment.

Imagine a positive integer number line (all possible integer values from 0 and above). The number line tends to infinity. For every integer you have, you can always add one to it (1 2 3 4 5 ...). In this set, which we shall call P, there are an infinite number of integers.

Now imagine a negative integer number line (all possible integer values below 0). The number line tends to - infinity. For every integer you have, you can always subtract 1. (-1 -2 -3 -4 -5...). In this set, which we shall call N, there are an infinite number of integers.

Good so far? Ok, so what about the entire set of integers, spanning from - infinity to + infinity. It's an infinitely large set. It isn't 2 x infinity, since such mathematics (if it even worked...which it doesn't) simply ends up with a value of infinity again.

To reduce it even more. There are an infinite amount of integers (both negative and positive) in the set of all integers. However between 0 and 1, there are an infinite amount of real numbers. So the set of all real numbers is the set of all integers (infinitely large) multiplied by infinity, which equals infinity?

No. Infinity is simply not a value. You could argue that in the equation "Infinity - Infinity", the first Infinity we are talking about is the set of all real numbers, and the second Infinity is the set of all real number between 0 and 1. So we are left with an infinitely large set made up of the sets of real numbers between every integer and it's neighbours, apart from 0 and 1.

It just doesn't work. Infinity is not a value.