Simple mathematical problem (?)

[AmateurScientist]

It brought a tear to my eye.

P*ssy.



AS

 

[AmateurScientist]

Thank you one and all! Humour noted!

Yes, AS, I do understand about axioms, theorems and proofs. I'm not trying to break the rules here, but use them properly as I go along. Perhaps I built my own stumbling block, as you will see.

[snip]

However I must point out quite clearly that I did understand right from the start about the original proofs provided for the theorem - I was not "missing anything" at all. I thought I said that a few times.

My issue, it appears, has been in making the cognitive leap from what I thought was mathematically logical in my own sense to arrive at the result previously obtained by others. I suppose, AS, that I was finding it hard to accept something that considered "axiomatic" when I could see no reason why it should be so!

I'm still working on this!

Zep,

Sorry to have doubted you or to have insulted your intelligence or educational background, if that's the way you took it. I didn't mean to.

I recall that you are an engineer, and I remember from my days as an undergraduate math major some animosity from engineering students towards mathematicians in my Differential Equations class. They seemed to regard those in pure math to be eggheaded doofuses, versus their practical applied math and problem solving selves.

With my own bias in that regard, I thought I detected a bit of engineer hubris and slight disdain for more abstract mathematics and number theory. Again, I apologize for my assumptions. They were probably unjustified and incorrect.

As far as .999... being equal to 1, you don't have to take it as axiomatic. You can prove it, just as so many have done in this thread. Otherwise, I'm not sure what you are referring to when you say that you see no reason for it to be axiomatic.

Anyway, you deserve an awful lot of credit for trying so diligently to digest everything that's been thrown at you in this thread. Some of it has been pretty mind-numbing.

Good luck again getting your head around this. It's probably something so simple it's staring you right in the face. You'll likely have one of those D'oh! moments soon enough. Let us know.

AS

 

[ceptimus]

Have you heard of the two part test that determines whether you should become an engineer or a mathematician?

For, the first part of the test, you are shown into a small kitchen that contains a faucet, stove and an empty saucepan on the floor. The test is to boil water. You pass this part of the test if you fill the saucepan from the faucet, and then boil the water on the stove.

The second part of the test is exactly the same, except that the saucepan is already full of cold water and in place on the stove. The budding engineer will simply light the stove. The mathematician will empty the saucepan, and place it on the floor. The situation is then the same as for the first part of the test, which has already been solved.

 

[AmateurScientist]

Have you heard of the two part test that determines whether you should become an engineer or a mathematician?

For, the first part of the test, you are shown into a small kitchen that contains a faucet, stove and an empty saucepan on the floor. The test is to boil water. You pass this part of the test if you fill the saucepan from the faucet, and then boil the water on the stove.

The second part of the test is exactly the same, except that the saucepan is already full of cold water and in place on the stove. The budding engineer will simply light the stove. The mathematician will empty the saucepan, and place it on the floor. The situation is then the same as for the first part of the test, which has already been solved.

LOL.

Engineers. Suckers.

AS

 

[LW]

I recall that you are an engineer, and I remember from my days as an undergraduate math major some animosity from engineering students towards mathematicians in my Differential Equations class. They seemed to regard those in pure math to be eggheaded doofuses, versus their practical applied math and problem solving selves.

And of course, a true mathematician scorns any practical use of mathematics...

I've seen a quote that was attributed to Euler. I couldn't google it out now so I'm not 100% certain of its contents, but the idea was:

"Abstract algebra is the purest form of mathematics since it does not have any practical applications at all."

I think that Euler rolled over in his grave the day when Lidl and Pilz published their textbook Applied Abstract Algebra...

(And yes, the book contains real-life practical examples of using abstract algebra to solve problems such as coding theory and cryptology. )

 

[AmateurScientist]

And of course, a true mathematician scorns any practical use of mathematics...

I've seen a quote that was attributed to Euler. I couldn't google it out now so I'm not 100% certain of its contents, but the idea was:

"Abstract algebra is the purest form of mathematics since it does not have any practical applications at all."

I think that Euler rolled over in his grave the day when Lidl and Pilz published their textbook Applied Abstract Algebra...

(And yes, the book contains real-life practical examples of using abstract algebra to solve problems such as coding theory and cryptology. )

LOL. I never thought anybody but mathematicians could ever make any sense of 99% of the text in my Advanced Algebra textbook in college. Hell, most of it was Greek to me.



Yeah, Applied Abstract Algebra--what a concept!

I'm with you, LW.

AS

 

[AmateurScientist]

It's always appropriate to question if I am wrong. In this particular case, you don't even need to take my word for it. My advice to anyone is go ask a professional mathematician or a professor of mathematics at the local university or college. Ask them two questions:

• Is 0.999... = 1?
  
• Is there any gray area or disagreement in the math community about the answer?

LOL. Several years ago I was in bar showing the simplest Let N = .999... , then 10N = 9.999... etc. proof of this theorem to a friend. I wrote it on a bar napkin and showed him.

After a cursory study of it, he handed it back and insisted I had performed a "trick" to reach the conclusion. I insisted there was no trick and tried my best to explain that this was nothing more than simple algebra.

Sitting near us was a lone gentleman who interrupted us. He mentioned that he couldn't help overhearing our discussion, but he was in fact a math professor at the largest university in town (it is especially known for its strong engineering and physics departments, especially aeronautical engineering). He offered to take a look.

I was astonished to hear him declare that something must be wrong. It didn't look right to him. I tried to explain to him, but he said he had had a few drinks and wasn't quite up to following along at the moment.

I laughed out loud as soon as we left. I learned this proof in the 7th grade, and I stumped this professor with a PhD in math. Never mind that he was drunk.



AS

 

[BillyJoe]

It's all those other forums where the fighting takes place. Those religious and philosophical types are real hard cases...

Except when they invaded us with that thread about Ian's signature regarding primary and secondary qualities.

 

[Zep]

I recall that you are an engineer, and I remember from my days as an undergraduate math major some animosity from engineering students towards mathematicians in my Differential Equations class. They seemed to regard those in pure math to be eggheaded doofuses, versus their practical applied math and problem solving selves.

With my own bias in that regard, I thought I detected a bit of engineer hubris and slight disdain for more abstract mathematics and number theory. Again, I apologize for my assumptions. They were probably unjustified and incorrect.

Background: I started doing an Engineering degree in Aeronautics, but switched to Science (double major in Computer Science and Information Systems, plus most of the Geology & Biology courses as well) when I realised I had more of a brain for bytes than making paper planes. So I suppose you could say I've had a foot in both camps. Maths was part of both these courses, but it was what you would probably consider typical undergrad stuff - I passed OK, I suppose!

However my personal interest in maths was increased with the boom in "chaos theory" studies (non-linear maths) of the 70's and 80's. This interest persists to this day, btw - I like to play with how this works... To me, it is the ideal mix of computer nerd stuff and abstract mathematics, i.e. fun.

Hope this puts things in perspective.


Befor I was an enjuneeer I coodnt even spel it.

 

[TillEulenspiegel]

Chaos theory eh? I also have a strange attraction for it myself.

Edit to add:
Besids being a smart ass , I remember the first program I ran to graphically represent the Mandlebrot set ( with certain parameters inputs by the operator) took hours to plot on an 8086, now it takes seconds

 

[Zep]

Chaos theory eh? I also have a strange attraction for it myself.

oh no... I feel a pun-run coming on...

Edit to add:
Besids being a smart ass , I remember the first program I ran to graphically represent the Mandlebrot set ( with certain parameters inputs by the operator) took hours to plot on an 8086, now it takes seconds

Been there, done that, got the TurboPascal code!

 

[Suggestologist]

So - since the arrow does in fact touch you, there must be something wrong with analyzing the number the way Zeno would have you analyze it.

That only points to the fact that numbers have no "reality" or "truth" outside of real usage. A different usage can point to a different conclusion. The arrow isn't set to stop at a particular place before it touches -- in fact it probably has enough propulsion to go much farther if no obstacle stops it -- so it has nothing to do with the .99... question; as formulated above.

When does 1 + 1 = 1? When you put one lion in a cage with one rabbit, you don't end up with 2 animals.

Limits were a trick to get away from violating Archimedes principle, because people used to use infinitessimals for calculus -- which don't go along with Archimedes' well-ordering principle (or something).

When you calculate a limit: You've got this number that is very small (epsilon), but larger than zero -- by definition!!! Then, what you do is you VIOLATE THE DEFINITION by pretending that this small number BECOMES zero. Sounds like an incoherent technique to me.

Limits depend and can be different depending on which side you take the limit from (i.e. for discontinuous functions). Because of this, what a limit "equals" cannot be said to mean the same thing as in: 1+1 "equals" 2. In other words, "equals" is overloaded when used with limits.

 

[Iamme]

I've been getting a kick out of all the replies...imagining posters with pencils in hand, feverishly trying to 'solve' this problem...which has an obvious error in it in the same way that that mathematical 'riddle' called "The case of the missing dollar" had.

Here is the error in the 5 or 6 steps equations: You can't come up with extra numbers past the decimel point when multiplying. What you are doing then is adding value to the equation which is not there.

When X = .999...10X = 9.99. Period! When you start adding .9's after it, the two halves of the equation no longer add up in step three. And the reason is easy, as I stated. You just can't start adding extra amounts (in this case...you can't add on extra .9, or .99, or.99999999999999, etc.

If you say 10X -X + 9.999-.999, there is your flaw. Right there. It should read: 9.99-.999. THEN, this will now = the right side of the equation. To say "recurrring" is a way of saying "anything goes"...and that's ridiculous. That's not math. That's chicanery.

 

[aerosolben]

When X = .999...10X = 9.99. Period! When you start adding .9's after it, the two halves of the equation no longer add up in step three. And the reason is easy, as I stated. You just can't start adding extra amounts (in this case...you can't add on extra .9, or .99, or.99999999999999, etc.

What is infinity - 1?

 

[xouper]

Suggestologist: ... what a limit "equals" cannot be said to mean the same thing as in: 1+1 "equals" 2. In other words, "equals" is overloaded when used with limits.

Your point has already been addressed and refuted several times in this thread. It is a mathematical certainty that 0.999... is exactly equal to 1, the same way 1+1=2. There is no overloading of the equal sign in this example.

Iamme: When X = .999...10X = 9.99. Period!

Wrong. You just flunked arithmetic 101.

To say "recurrring" is a way of saying "anything goes"...and that's ridiculous. That's not math. That's chicanery.

No. You're the one being ridiculous. Learn some math and quit wasting people's time with your nonsense. Same goes for Suggestologist.



Edited for spelling.

 

[patoco12]

The great debate that is .9~ =? 1

Creationism:

The Mathematicians created a decimal notation for ease of use and to represent numbers that were difficult to represent in fractional form. When concerned with infinite decimal numbers, they created infinite lengths. There was no process involved; a higher being (math geeks) just waved their fingers and infinite decimals were formed in their image of what an infinte should be. The number .9~ was created. But when looking for a fractional equivalent, the math geeks could not find an intuitive number. So out of the ground was born an equivalent companion for it: 1.


Evolution:

Mathematics has changed over thousands of years through tiny mutations in notation and usage. Different ways at "looking" at the numbers has caused different interpretations. Only pragmatic number notations survive. We call this Numerical Selection. Infinite decimals have intrigued evolutionists, as the journey from .9 to .99 to .999 to .9999 to .9999... is a long one. When confronted with the possibility that .9~ = 1, evolutionists continue to search for the "missing link" between the two. To this day, this missing link both eludes and haunts them.



edited to add a smiley to make the joke obvious

 

[patoco12]

..this will now = the right side of the equation.

Don't ever mix notation with English in a Math forum; you'll be flamed to no end! Luckily, this forum doesn't come close (that's why I like it).

Remember, point nine repeating = one!

 

[Iamme]

Notice how there are about 500 posts regarding this question? This proves that nobody wants be an idiot.

And now that I brought THAT up...the answer I gave yesterday still really never got to the heart of the question. Not really.

I actually gave this 'problem' (equations) some thought this morning. Here is the answer:

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.

Yes, this problem is a result of a trick question. It is like a magic act. It's like an illusion. Here is why the illusion works. I already explained that .999 was chosen because it sidetracks you bexcause it is NEARLY 1. But the cause for the discrepency (how can .999=1, when we really know it doesn't?) lies in the fact that the algebraic equation is really not a 'equation' per what most of us think an equation is. An equation begs to be solved. An equation that can only produce one correct answer for a value of X could be called a closed equation. The equation WE were presented with was an 'open' one.

Let me illustrate an example of one that is closed that only has one answer that will work for X: 10X-3=27. X has to =3.

O.k., now look at the equation the author digs out of thin air. Note that a value was already established for x, unlike the equation of mine that needs you to FIND X. The author already TOLD you what X was. THEN, they presented us in step #3 an OPEN equation. Such an equation is not the type that you have to solve. It is an equation that has alREADY been solved. The left half of the equation = the right half of the equation.....(get ready) for no matter WHAT value you ascribe to X.

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!"

If you had first saw THIS equation presented...you probably would have just thought this thread was silly. Maybe 3 people would have responded, and pointed out the error. BUT...being that .999 recurring was used, and then making it out that instead of 5=1...that .999=1...that caused many of us to wonder if it could really be true. So, you (we) became more of an unsuspecting victim just because of the value that was chosen, which made the problem seem more vexing than it really was.

Bottom line: There really never was an 'equation'. If you still have to scratch your head...just look up and stare at my 5-line illustration using 5, instead of .999 recurring.

(Further note that line 3 in the equations does work correctyly with the number 5. It becomes 50-5=45. The number 1 will work. So will 2, so will 3,4,5,6,7...so will decimals. Any number or fraction works. The only reason that .999recurring does not work is that you allow yourself to turn .990 into .999, which is not correct. But this is all besides the point, anyway, per the reasons I gave in my post. .999 recurring was chosen as the number, just to complicate matters and throw you off.)

 

[LW]

Notice how there are about 500 posts regarding this question? This proves that nobody wants be an idiot.

May I suggest to you that you read through those 500 posts before posting again on this thread.

But here's a short summary: 0.999... = 1 when standard mathematical definitions are used (several different and correct proofs are within the 500 posts), and 0.999... != 1 when Suggestologist's own definitions are used.

 

[xouper]

Iamme: Here is why the illusion works. I already explained that .999 was chosen because it sidetracks you bexcause it is NEARLY 1.

We already know that 0.999 (without the ellipsis) is nearly equal to one. We also know that 0.999... (with the ellipsis) is exactly equal to one.

But the cause for the discrepency (how can .999=1, when we really know it doesn't?)

No one here has said 0.999 = 1. What we have said, however, is that 0.999... is equal to one. The ellipsis makes a big difference.

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

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.

Bottom line: ...

Bottom line is, you have no clue what you are talking about. I'll say this again - go learn some math and quit wasting our time here with your nonsense.

If you think 0.999... is not equal to one, then you are also claiming there exist two positive integers A and B such that that A / B = 0.999... and that A is not equal to B. Since you seem to think you're right and mathematicians are all wrong, then find us that A and B.