[split] 0.999... equals 1

[Meatball]

One apple minus one apple is no apples.
Fourteen zebras minus fourteen zebras is no zebras.
One daydream about dancing under the sea minus one daydream about dancing under the sea is no daydreams about dancing under the sea.
Three **%*##! minus three **%*##! is no **%*##!s.

Thus, one might conclude that,
One (.999...) minus one (.999...) is no (.999....)s.

[Violet]

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 infinity is not a value at all, then the value of 0.9^ is 0.9. You are using the concept of infinity to describe the value of a number, and in doing so make that number's identity uncertain... Impossible to calculate. I do not see where I contradicted myself in this instance.

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.

So you are saying that 1/0 and 2/0 can be calculated? If something takes an infinite amount of time to calculate, it is because it is incalculable. We call these numbers 'undefined'. What is the answer to 1/0? Undefined. Oh wait... that would be calculable because it only takes an infinite amount of time to calculate? lol?

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:

/sigh,

Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.

Yes, I read the entire article. All the way down to this quote, which I posted before, probably with hide tags like I am doing now:

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Proving or disproving the existence of infinitesimals of the kind used in nonstandard analysis depends on the model and which collection of axioms are used. We consider here systems where infinitesimals can be shown to exist.
In 1936 Maltsev proved the compactness theorem. This theorem is fundamental for the existence of infinitesimals as it proves that it is possible to formalise them. A consequence of this theorem is that if there is a number system in which it is true that for any positive integer n there is a positive number x such that 0 < x < 1/n, then there exists an extension of that number system in which it is true that there exists a positive number x such that for any positive integer n we have 0 < x < 1/n. The possibility to switch "for any" and "there exists" is crucial. The first statement is true in the real numbers as given in ZFC set theory : for any positive integer n it is possible to find a real number between 1/n and zero, but this real number will depend on n. Here, one chooses n first, then one finds the corresponding x. In the second expression, the statement says that there is an x (at least one), chosen first, which is between 0 and 1/n for any n. In this case x is infinitesimal. This is not true in the real numbers ® given by ZFC. Nonetheless, the theorem proves that there is a model (a number system) in which this will be true. The question is: what is this model? What are its properties? Is there only one such model?
There are in fact many ways to construct such a one-dimensional linearly ordered set of numbers, but fundamentally, there are two different approaches:
1) Extend the number system so that it contains more numbers than the real numbers.
2) Extend the axioms (or extend the language) so that the distinction between the infinitesimals and non-infinitesimals can be made in the real numbers.
In 1960, Abraham Robinson provided an answer following the first approach. The extended set is called the hyperreals and contains numbers less in absolute value than any positive real number. The method may be considered relatively complex but it does prove that infinitesimals exist in the universe of ZFC set theory. The real numbers are called standard numbers and the new non-real hyperreals are called nonstandard.
In 1977 Edward Nelson provided an answer following the second approach. The extended axioms are IST, which stands either for Internal Set Theory or for the initials of the three extra axioms: Idealization, Standardization, Transfer. In this system we consider that the language is extended in such a way that we can express facts about infinitesimals. The real numbers are either standard or nonstandard. An infinitesimal is a nonstandard real number which is less, in absolute value, than any positive standard real number.
In 2006 Karel Hrbacek developed an extension of Nelson's approach in which the real numbers are stratified in (infinitely) many levels i.e, in the coarsest level there are no infinitesimals nor unlimited numbers. Infinitesimals are in a finer level and there are also infinitesimals with respect to this new level and so on.
All of these approaches are mathematically rigorous.

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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.

Yes, I read that it was the original description of it... yet surly you should know that it was under that description that Calculus was invented.

Anyway, I did discuss this subject with several mathematicians. Instead of calling me a moron (among other things): Target my arguments and statements. Am I calling you a moron in my dissent of your arguments? Not that I can tell. Do I suggest that you haven't researched this subject? Also not that I can tell. Have you proven to me yet that this inequality is equal? You have not.

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.

I would like to do so if you continue to not prove your statements. I told you before that I don't doubt that the mathematicians are right... I simply have to make it right by me. As of yet: I do not see it. Why wouldn't you ask questions of mathematics to mathematicians?

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.

limitless or endless in space, extent, or size; impossible to measure or calculate

Can something be infinite only in size? Open your mind. .9^ is infinite in length. oo is infinite in size. Arrogance can be infinite in sheer incalculability. Seriously... and honestly... infinite is an adjective... it is not a noun. When you modify a value you sticking infinite on it: you have made that value impossible to calculate. Finites are not impossible to calculate, so from the very beginning .9^ CANNOT equal 1... lest an infinite be finite which would declassify it's infiniteness.

This is my proof, the proof of the Identity's Equality (That I am me and not you... remember?). Only by canceling out that which cannot be calculated can we calculate.

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.

Only for finites. This only applies to the incalculable. Referring to what I said above: If you cancel out the infinite, then you have made the number finite, and are no longer proving an infinite. Unless you are suggesting that infinities are finite? Or that there really IS an answer to 1/0?

By canceling out impossible to solve things, you make equations solvable. Thus you can get your answer to the equation via this method. So you are not proving that an infinite is equal to a finite... you are proving that the remaining equation (now that you have removed that troublesome infinite) is equal to a finite

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...

And you can't have an infinitely long penis... with a head? The number on the 'end?' is a descriptive quality to the number, insomuch as the head is a descriptive quality to the penis. Lest the number be non-descriptive (like 1/0?), you must include those describing digits.

Funnily enough, I have gotten my proofs of different answers from 10x-1x vs 9x by a calculator. With finite numbers: you're fine. With incalculable infinites? Not so much.

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.

Interesting... I've always done quite well in mathematics. Perhaps they don't teach these amazingly simple mathematics (That I have been using?) to young girls about to graduate high-school mathematics?

If infinity is not a value: then don't use it as part of the value for a number .9^ cannot be multiplied, divided, subtracted, or added... because it would take an infinite amount of time to calculate, and "it just doesn't work".

Anyway, infinity is not by itself a number... it is a description of "a number endlessly big, or long, or etc.". By stating something like 1/oo, we are suggesting that the number we are dividing is endlessly huge... by 1/.9^, we are suggesting that the number is endlessly long.

Etc. Please understand that infinity is the value of endlessness, unfathomability. It is he value of being without limit. Using it to describe a number (see .9^) is removing that number from being limited... making the fathomable decisively not. Numbers like .0^1 are to show that there is an unfathomable, limitless number of zeros before a one. This is not an infinite number with an end... it is a finite number placed unfathomably in the distance.

That's really all.

[Ephrium]

Saerulees, why did you not read my post?

0.99r Is just a quantity. This quantity can be deducted by the same quantity.

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On the other hand, I am having problem figuring out if it can be multiplied or divided. Hmm..

[Violet]

I read both your's and Meatball's, and wholeheartedly agree

Why do you ask? Anyway, if it can be added or subtracted: then it can be multiplied or divided. Multiplication and division are just 'shortcuts' for adding and subtracting, after all

[Ephrium]

perhaps I have misinterpreted. When I read your post I thought you still meant an infinite string cannot cancel out another infinite string, even though they are the same.

[Violet]

When you asked, i looked over my post for a good 5 minutes trying to figure out where i'd contradicted that The end might seem like it, but I was being completely hypothetical (If infinity is not a value) Perhaps that's what you misinterpreted?

I'm sure I could have been clearer, but I'm only human

[Rhizomorph13]

Sae,

.9r is a finite number because it is less than 1.1r and greater than .89r. I don't know if you are having trouble with this or not, but the syntax of some of your posts seem to lead to the conclusion that .9r is somehow not a finite discreet value.

Rhizo

[Violet]

Hmm, i thought I had made it clear that .9^ is infinite in extent...

limitless or endless in space, extent, or size; impossible to measure or calculate

1.1^ and .89^ are also infinite in length. That it is not infinite in size does not make it any less infinite in length We can safely say that .9<.9^<1. An interesting thing about a number like .9^, is that it is always getting bigger, but never reaching a certain size. To graph the number, you would see that it approaches one, and the closer it gets: the further it curves away from it.

Much like a loading bar with no end

[Rhizomorph13]

Sae,

But .9r is always less than 1.1 and always greater than .9. it is bound in and therefore not infinite. Adrian talked about the difference between infinitely large and infinitely long.

.9r !<1 but .9r = 1 by the proofs shown by me and Adrian. I doubt you will listen to me either. Just for the record I see what you are saying and thought something similar at one point. I scoured the internet looking for anything that would help me bring down the proof but it is very well supported on the internet. Sometimes established truths are such because they are, ya know, true.

Rhizo

[Violet]

But both are infinite. Infinite is not applicable to only one thing. Its definition is 'without limit'... and so all it does is modify a concept, in much the way one might expect any other adjective, adverb, or prepositional phrase to do.

I understand that it is probably true... but I require a good reason to believe it is true. That other people think so just isn't good enough for me. I trust that they are probably right... but I also trust that they are right for a reason. I want to see that reason.

I don't deny that establishment is sometimes true... but nothing is true simply because it has been established, as religions should be good evidence of.