Simple mathematical problem (?)

[xouper]

I missed one -

Iamme: The reason why everyone is so hung up on this problem is the fact that .999 was used. It is so close to the number 1. AND, to make it seem MORE complex...by adding 'recurring' to it even FURTHER causes us to go blind by the illusion.

No, it is only making YOU blind. Mathematicians can see quite clearly that 0.999... is exactly equal to one.

 

[Iamme]

Xouper---Ya, right. Got any more good ones for me? How big was that fish you say you caught?

 

[Iamme]

Ya...and 5 = 1 also. (I proved it...above)

 

[Martin]

Wrong. You made an error in that last step. Just because 9X=9X in no way implies that X must be 1. The most you can say from 9X=9X is that X=X

To be fair, the same error appears in the OP. Lamme was addressing that, it seems.

Of course, the typo was corrected later and several other proofs offered. Had Lamme bothered to read on he would have realised that himself.

 

[Iamme]

Xouper---Sorry. I missed seeing your post right after my post. I give up. I quit. I have explained it two different ways.1. That by allowing (recurrent) is non-sense as you are alowing yourself to add value to 1/2 of an equation. 2. That that third equation is not really a problem solving type equation. It's just a matter of fact. Then YOU say all I can reduce the last equation to is X=X. Yes. So? X can equal any number. The only way you guys have made .999 =1 is by cheating in step 3. But go ahead and keep believing this goofy theory. Let somebody else try to change your minds. If you continue to believe some 'expert' who has proven that .999 =1, you go ahead, while I'll believe that crop circles really CAN exist based on the notion that if a real $20 bill can be counterfeited...and we know that there were REAL $20 first....that crop circles likewise could be a copy of the real thing, also. So there.

 

[Iamme]

Martin---Hi. What was they typo you speak of. I am flying around 6 forums on 2 message boards on limited time and I couldn't read, sadly enough, ALL 500 posts to injest them all. I read several though on page one, when I felt I had enough insight to give my own two-cents worth...which now appear to not be worth two-cents.

 

[geni]

The first proof contains a typo. here is the corrected version:

X = 0.999(recurring)
10X = 9.999(recurring)
10X - X = 9X
But, by virtue of the first two equations, 10X - X also equals 9 (the recurring 0.999's cancel out)
So, since 10X - X = 9X and 10X - X = 9,
9X = 9
X = 1

 

[Martin]

Martin---Hi. What was they typo you speak of

The proof offered in the OP goes as follows:

X=0.999(recurring)
10X=9.9999
10X-X = 9X
9X=9X
X=1

It is this which your 5=1 'proof' appears to follow. But there's a typo in the third line. It should read:

X=0.999(recurring)
10X=9.9999
10X-X = 9
9X=9
X=1

 

[xouper]

Iamme: But go ahead and keep believing this goofy theory. Let somebody else try to change your minds. If you continue to believe some 'expert' who has proven that .999 =1, you go ahead,

I have already proven that 0.999...=1, and so have several other people in this thread. You, on the other hand, have proven nothing except perhaps that your understanding of math is severely flawed.

 

[xouper]

Iamme: The only way you guys have made .999 =1 is by cheating in step 3.

I used the geometric series theorem in my proof and there was no cheating in any of the steps. Try reading the rest of the thread before running your mouth.

And by the way, it's 0.999...=1, not 0.999=1. Please do not omit the ellipsis when you talk about this equality.

 

[patoco12]

Now, let's do the math problem all over again using a new value. Let's use 5, instead of .999 recurrring:

X=5
10X=50
10X-X=9X
9X=9X
X=1

Now do you see? We can NOW say in a 6th step, "Therefore 5=1!"

You've assigned X to be equal to 5. How, then, can you say that X is equal to 1? Look again at your work. All you've shown is that 45 = 45. And you really haven't even done that, as there is a mistake in your algebra, as you didn't catch the typo that was corrected on about page 2 of this thread. I would at least read that far before jumping into the debate.

In the future, please no algebra tutorials. If you would have read the rest of this thread, I think you would agree that nobody needs it (not even those arguing that .9~ != 1).

 

[ebola]

1 - 0.999... = 0.000... = 0

Therefore, 1 = 0.999...

Please stop now. I am begging you. Please stop now.

Eric

 

[Brickroad]

I have always thought that there had been some sort of trick to the .999... = 1 equation. I always dismissed it as a minor curiosity in mathematics.

However, seeing all the various proofs offered in this thread has corrected my erroneous reasoning. The tireless efforts of the more rational posters in this thread have not, therefore, fallen entirely on deaf ears.

I have a greater understanding on the concept of infinity, among other things, after having read this thread. And I find it highly entertaining as well!

 

[TillEulenspiegel]

I hate infinity, its like tryin to nail jello to a wall

 

[BillyJoe]

Yellow,

This forum actually introduced me to the fact of .9~ = 1
And to infinity not being a process.
On another thread I discovered the existence of and the mechanism for thunderless lightning.

I was as thick as a brick when I first got here and now....well.....er....
Well, I'm walking a little more confidently down that road.

BillyJoe.

 

[Iamme]

Xouper---I aplogize for getting you so steamed, about me and others not comprehending the concept.

My problem (can't speak for the others) is that I did not realize that the term 'recurring', or 'recurring decimal' is the same thing as 'ad infinitum'. If I would have known this was ad infinitum, I wouldn't have bothered posting, probably.

I presumed that when I saw in the equation that X=0.999...(recurring), that in the next step of the equation where it became 10X. that instead of 0.999 becoming 9.990, it became 9.999. Hence, the addition of another 9. I then would have presumed that if the equation were 100X, or 1000X, that one would add an additional 9. Anyway, sorry...now I know.

So now, this is what I don't get: What does the initial thread starting equation prove? Why not just say that 0.999999999999999999999999999..to infinitum = 1, and let it go at that? In the equation (the thread-starting equation) where X= 0.999...(recurring), I see step 3 is the same as step #4. The left side of the equation equals the right side of each of the equations. X was already told to us in advance. X could be any value and work. Therefore, I don't understand what the equation proves. No where in the equation do I see O.9999999...recurring, turning into 1, by virtue of the equation.

I tried to grasp 0.9999999999999999...recurring) in a comprehensive manner outside of strictly mathematical theory. Here it is: If you take the entire universe, and you subtract one quark from it...do you have 1 universe, or do you have less than 1 universe? You have less than 1 universe. Obviously. But to express this, you would have to say that the remaining universe is 0.99999999999999...out trillions and trillions of decimal points. BUT...there would be an end to the decimals, eventually. It would indeed be an answerable finite number. IF you then disected the quark into a quark size of the quark itself, you would have to say that the remaining universe is , once again, 0.99999999999999999999999999999999...out to trillions and trillions of decimal places, I believe doubling the decimal places you had already put down with the quark missing. BUT, even with this last scenario, you would still hacve a FINITE number of 9's after the decimal point.

So, what could cause a universe to even HAVE 0.999999999999999999999...ad infinitum? Nothing that I can tell. IOt's like, no matter whar you subtracted...even if it was trillionths of the one quark, you would still come up with a finite number that starts 0.99999999999999999999999.Therefore, this whole thing seems silly. It's theoretical only. It's like mathemeticians are trying to show they are smart, by bringing up something useless. What could anybody analyze, in the universe that is only 1 quark out of the universe, and be talking about anything with substance?

But I will close by saying that from my reasoning about the universe...forgetting equations...that 0.9999999999...out to ad infinitum does indeed have to equal 1, by virtue of what I just said, that by removing the smallest of the small of the universe would leave you with a FINITE number, eventually. The only other explanation for 9's going out to infinity, if it is 1.

 

[DanishDynamite]

Iamme:

So, what could cause a universe to even HAVE 0.999999999999999999999...ad infinitum? Nothing that I can tell. IOt's like, no matter whar you subtracted...even if it was trillionths of the one quark, you would still come up with a finite number that starts 0.99999999999999999999999.Therefore, this whole thing seems silly.

No, it isn't silly. Not at all. Precise definitions is the cornerstone of mathematics.

It's theoretical only. It's like mathemeticians are trying to show they are smart, by bringing up something useless.

How many times throughout history have we heard this before?

Iamme, mathematics isn't useless, and never has been. Even esoteric mathematics which seems far removed from any practicle application. There are very, very many examples of this.

What could anybody analyze, in the universe that is only 1 quark out of the universe, and be talking about anything with substance?

The Universe doesn't enter into the equation. We are talking about mathematics here, the foundation and self-consistency of same. If it isn't self-consistent, it is of no use to anybody.

 

[Iamme]

Danish Dynamite---I never SAID that math was useless.

I said that with this particular example, it seems silly. What is the practicality to this, mathematically, if I might ask? If math has nothing to do with the universe, then what does it have to do with? By 'the universe', I mean not just the expanse, but all that is in it. I gave the example that even the smallest entity CAN be expressed with a finite number of .9's (albeit trillions of them, but nonetheless finite). You tell me what topic would come up in mathematics that they would have to know what goes beyond several trillion (finite though) .9's?

Do they go, "Hmmmm, let's see....0.9999999999999999999999999999999999 X 0.9999999999999999999999999999 = hmmmmm...what should we put down?....hmmmm...let's just put a 1 down so we don't have to write out so many 9's?"
I doubt it. So, if you could just give me a practical example, I would appreciate it. But try to keep it simple. I don't see where lines and lines of equations would be necessary. I'm just trying to grasp the practicality of this whole thing, as opposed to genius people who may conjure up methodologies to stump lay people. Sort of like in the medical field where they call common name things something in their own pig-latin version, like it's an inside joke. Same with lawyers and their vernacular.

 

[ceptimus]

The equivalence of 0.999... and 1 is important in Cantor's diagaonal proof. Google on it if you're interested.

 

[DanishDynamite]

Iamme:

Danish Dynamite---I never SAID that math was useless.

I said that with this particular example, it seems silly. What is the practicality to this, mathematically, if I might ask?

Your question makes no sense. Mathematics isn't concerned with practicality. It is concerned, among other things, by consistency.

If math has nothing to do with the universe, then what does it have to do with? By 'the universe', I mean not just the expanse, but all that is in it.

The amazing applicability of math to the Universe is a philosophical question of much discourse. However, math as such, doesn't care.

I gave the example that even the smallest entity CAN be expressed with a finite number of .9's (albeit trillions of them, but nonetheless finite). You tell me what topic would come up in mathematics that they would have to know what goes beyond several trillion (finite though) .9's?

Consistency.

Do they go, "Hmmmm, let's see....0.9999999999999999999999999999999999 X 0.9999999999999999999999999999 = hmmmmm...what should we put down?....hmmmm...let's just put a 1 down so we don't have to write out so many 9's?"

No. Please, Iamme, read a few books on math. Try to understand that without precise definitions and precise proofs, math would be meaningless.

I doubt it. So, if you could just give me a practical example, I would appreciate it. But try to keep it simple. I don't see where lines and lines of equations would be necessary. I'm just trying to grasp the practicality of this whole thing, as opposed to genius people who may conjure up methodologies to stump lay people. Sort of like in the medical field where they call common name things something in their own pig-latin version, like it's an inside joke. Same with lawyers and their vernacular.

A practical example of what? That mathematics has had an influence on practical matters in the world? The list would be without end.

BTW, do you know the origin of writing? It stems from mathematics or more proberly from accounting.