New Proof that 1 = .999999999 Repeating

[dornick]

Originally posted by: 91TTZ

Originally posted by: dornick
You're completely correct up until that last sentence. What do you mean by fallen short?

Have you taken calculus yet? Back in the day, my reasoning was identical to yours, until I took calculus and realized I was wrong. If you haven't gotten there, trust us and you'll see If you still won't let it go, I recommend that Dr. Math link I put in my edit.

I'm saying that a given number will always be smaller than a number that has a larger value in the previous (leftward) placeholder.

Some fields in math must go an an assumption. Otherwise they won't work. They may be right 99.999R% of the time but they won't be right 100% of the time. Take Newtonian physics for example. Nobody would have thought that as you increase in speed the laws of physics can begin to follow other principles. But Einstein formulated that as you approach the speed of light, you gain mass.

The assumptions that form the basis of math are far from saying certain repeating decimals are equal to whole numbers, that sort of stuff is proven. And your physics comment is irrelevant. Physics uses math to describe our universe. Because it can give an inaccurate description at times doesn't mean the math is wrong.

btw, since you didn't answer my question about calculus, I'm going to assume you haven't taken it and therefore you aren't exactly qualified to be trying to overthrow parts of math.

 

[91TTZ]

Originally posted by: dornick
btw, since you didn't answer my question about calculus, I'm going to assume you haven't taken it and therefore you aren't exactly qualified to be trying to overthrow parts of math.

I took Calc in HS, honors class crap. But I didn't think that would really help anyone's argument. I could also demand to ask what someone's IQ is to see if they have the mental horsepower actively partake in a thinking contest, but that would be rude, wouldn't it? Anyway, I've been in honors classes since 2nd grade (we got to play with Logo on the Vic 20, W00t!)

 

[91TTZ]

By the way, I think that merely regurgitating what you've learned in school doesn't exactly qualify someone to be an intelligent person. It's their ability to think for themself that determines that. You could have been Einstein's little lackey, but that doesn't exactly help your case.

 

[TuxDave]

Originally posted by: 91TTZ
Here's a thought-

1 = 1

.999... = 1 - (1/infinity)

Since 1/infinity is a number, no matter how infinitely small, we can therefore say that 1- (1/infinity) is slightly less than 1, coming up short by an infinitely small margin.

Therefore, .9999... does not equal 1

In your way of thinking, 1/infinity > 0. In my mind of thinking 1/infinity = 0.

 

[91TTZ]

Originally posted by: TuxDave


In your way of thinking, 1/infinity > 0. In my mind of thinking 1/infinity = 0.

I agree. I think that 1/infinity would be the smallest non-zero number possible.

 

Originally posted by: silverpig

Originally posted by: 91TTZ
I still like my argument that .9999 repeating = the largest possible fraction less than 1. It misses being 1 by the smallest possible amount.

I know for all intents and purposes math considers .9999..... to be 1, so this is more of a logic/philosophy argument.

*sigh*

You're wrong. It's not philosophy, it's math. 1 = .999... and that is that.


This thread ends *now*

Nope, you're wrong and 91TTZ is right! I wonder why there's such thing as philosophy of mathematics if you were right!

 

[TuxDave]

Originally posted by: 91TTZ

Originally posted by: TuxDave


In your way of thinking, 1/infinity > 0. In my mind of thinking 1/infinity = 0.

I agree. I think that 1/infinity would be the smallest non-zero number possible.

I believe I'm familiar with your school of thought. I believe there does not exist a smallest non-zero positive number. Just like the other puzzle, if you have to parallel lines of infinite length and you rotate one ever so slightly. Where would the first point of contact be? I say the 'first point' of contact doesn't exist. But your school of thought derives numbers like the existance of a 'smallest positive non-zero number'.

 

[TuxDave]

Also, with your mindset, how do you resolve the puzzle where there are an infinite number of halfway points between here and there, how can you get there if you can never cross that 'last' halfway point.

 

[mchammer187]

Originally posted by: 91TTZ

Originally posted by: TuxDave


In your way of thinking, 1/infinity > 0. In my mind of thinking 1/infinity = 0.

I agree. I think that 1/infinity would be the smallest non-zero number possible.

a smallest nonzero number cannot exist in the decimal system

its .0....................1 all over again

 

[Coro Dominicano]

Simple..

x = 0.99999...

10x = 9.99999....
- x = 0.99999...
9x = 9
x = 1

Therefore
x=0.9999..=1

 

[dornick]

Originally posted by: 91TTZ
By the way, I think that merely regurgitating what you've learned in school doesn't exactly qualify someone to be an intelligent person. It's their ability to think for themself that determines that. You could have been Einstein's little lackey, but that doesn't exactly help your case.

I ain't doin no regurgitation. As far as I remember, we only discussed this once, and that was back in algebra when I was firmly entrenched in your way of thinking.

If you don't see how calculus helps, I can only ask what your class did. Let's start by formally defining .9 repeating, as nobody really seems to understand what it means.

.9R = lim (as n->infinity) of the sum (from 1 to n) of the geometric series 9/(10 to the n)

Using the formula for infinite geometric series, you get 1.
Appealing to the idea that "there will always be space" doesn't make much sense when you never stop taking 90% of that space away. But thinking about it in terms of space and not infinity, you realize there is none because if there were, you could find another number between the two. This is the true definition of equality

 

[ActuaryTm]

Not surprisingly necessary yet again.

 

[TuxDave]

Originally posted by: ActuaryTm
Not surprisingly necessary yet again.

lol

 

[nCred]

Originally posted by: Coro Dominicano
Simple..

x = 0.99999...

10x = 9.99999....
- x = 0.99999...
9x = 9
x = 1

Therefore
x=0.9999..=1

That says nothing, it´s like saying

9.99999.... = 9.99999....
-0.99999....
9 = 9

I think.. umm..

 

[Howard]

Originally posted by: dornick

Originally posted by: 91TTZ
By the way, I think that merely regurgitating what you've learned in school doesn't exactly qualify someone to be an intelligent person. It's their ability to think for themself that determines that. You could have been Einstein's little lackey, but that doesn't exactly help your case.

I ain't doin no regurgitation. As far as I remember, we only discussed this once, and that was back in algebra when I was firmly entrenched in your way of thinking.

If you don't see how calculus helps, I can only ask what your class did. Let's start by formally defining .9 repeating, as nobody really seems to understand what it means.

.9R = lim (as n->infinity) of the sum (from 1 to n) of the geometric series 9/(10 to the n)

Using the formula for infinite geometric series, you get 1.
Appealing to the idea that "there will always be space" doesn't make much sense when you never stop taking 90% of that space away. But thinking about it in terms of space and not infinity, you realize there is none because if there were, you could find another number between the two. This is the true definition of equality

I already covered this in my post, which he conveniently ignored. That, or he denies the formula for the sum of a geometric series.

EDIT: I'll try to clear it up. 91TTZ, do you believe in a non-zero infinitely small number?

 

[91TTZ]

Originally posted by: Howard

EDIT: I'll try to clear it up. 91TTZ, do you believe in a non-zero infinitely small number?

Yes. Take any number and keep on dividing it in half, forever. The remaining number will endlessly be divided in half, but you'll never get to zero.

 

[dornick]

You might never actually calculate zero if you did this for all eternity, but the limit is zero, and that's what we're talking about here.

 

[DrPizza]

Originally posted by: nakedfrog

Originally posted by: 91TTZ
Interesting link:

http://descmath.com/diag/nines.html

:thumbsup:
I think that covers it all pretty well.

Not really... read the "about me" for the author:

I switched my major from arts to mathematics, and within two years flunked out of school. My main problem was that my work on the Calculus put me on the losing side of an argument that had been raging in the mathematics community for the last century. This conflict, of course, is the schism between logicists and intuitionists.

As someone who majored in mathematics, I'd like to point out that his "main problem" is far from sufficient to cause someone to fail out of college.

more:

Anyway, after losing my argument. I failed school and spent the next decade a half working custodial and clerical jobs for near minimum wage. In the 90s I was fortunate to find a company that let me hack on their computers as part of my minimum wage data entry job. Since then, I have been able to pay rent by working with companies willing to hire second rate programmers at below market rates.

greaaaaaat.... you're using a 2nd rate college flunkie programmer as a source to back your argument... Couldn't find someone who graduated from college?

 

[frank84]

and..

WHY IS THIS IMPORTANT????

 

[DrPizza]

Originally posted by: TuxDave

Originally posted by: 91TTZ

Originally posted by: TuxDave


In your way of thinking, 1/infinity > 0. In my mind of thinking 1/infinity = 0.

I agree. I think that 1/infinity would be the smallest non-zero number possible.

I believe I'm familiar with your school of thought. I believe there does not exist a smallest non-zero positive number. Just like the other puzzle, if you have to parallel lines of infinite length and you rotate one ever so slightly. Where would the first point of contact be? I say the 'first point' of contact doesn't exist. But your school of thought derives numbers like the existance of a 'smallest positive non-zero number'.

I agree that there's no smallest positive number. PROOF:

Assume there *IS* a smallest positive number.
A positive number divided by a positive number is still a positive number.
Divide the smallest number by 2... it's now half the original size. But wait... it it's half the original size, then it's smaller than the smallest positive number. Since it's also positive, it leads to a contradiction. Therefore, the assumption must be false.

 

[DrPizza]

Since the thread is getting boring quickly...

1/2 + 1/4 + 1/8 + 1/16 + 1/32 +... = 1 (or .9999... if you wish )
Simple to see (for the non-calculus people)
While you're always adding on an amount, you never reach 1 with a finite number of terms, because every new term added in the series only brings it 1/2 of the way closer to 1 than the current sum.

1/2 + 1/3 + 1/4 + 1/5 + 1/6 +... (the harmonic series) gets larger and larger without bound (becomes infinitely large)


But, how about this...
1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + 1/5^2 + ... = (pi^2)/6
wtf did pi come from?? (well, I recalled this one when someone else mentioned pi above)
But, pi is the ratio of a circle's circumference to its radius. What's that got to do with a series?

For those who don't agree that .999... = 1
I'll stop thinking you're simply mathematically challenged (mathematically retarded is what I was actually thinking, but I don't want to insult the many fine retards who are at least smart enough to recognize which people to believe) if you can demonstrate why the last series I listed sums up to (pi^2)/6 (or even "infinitesimally close" to that value)


hint (in case you're googling it) Jacob Bernoulli proved the sum converged. (more than 300 years ago) Leonard Euler found the sum of the series a little less than 300 years ago.

 

[dornick]

euler (sp?) was pretty damn smart

 

[otispunkmeyer]

5+7 = 11

 

[DrPizza]

Originally posted by: dornick
euler (sp?) was pretty damn smart

I'll bet the majority of people who don't understand that .999... = 1 can't even pronounce his name correctly.

And, yeah, Euler was pretty darn smart. And, wtf was up with the Bernoulli family?! A couple of generations of mathematical geniuses and offspring.

 

[ActuaryTm]

Some of the responses - on both sides of this argument, to be honest - are so completely laughable that I am reminded of the infinite (no pun) wisdom of one Dr. P. Venkman :

• "Human sacrifice, dogs and cats living together - mass hysteria."

As such, please revisit the aforementioned graphic.