.99999 does not equal 1

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Raist

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Re: .99999 does not equal 1
« Reply #600 on: September 05, 2008, 09:12:31 AM »
Indeed, 0.9999 does not equal 1 so we have to wonder what this thread is all about.  ;)

If we consider the real question - does 0.999... equal 1 then I have just one thing to say:

If it doesn't, give me the number in between.  :P

Of course, there are 31 pages in this thread and someone may have said this already.

Well, there's no integer in between 5 and 6 - so are you claiming 5=6?

Why does there have to be a number in between 0.999... and 1? Maybe 1 is right above 0.999...

I did not say integer, I said number. However, I take your point and should have been more specific and used the term real number.

Well, then you need to prove that between any two real numbers there's a third and distinct one. Obviously your claim works for some types of number systems and not for others, so you need to show it works for the reals in particular. For all I know the reals work just like the integers.

Tread carefully - in the hyperreal numbers for instance the smallest number greater than zero is quite well defined. There is no number between it and 0.
There are infinite real numbers between any two numbers.

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Parsifal

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Re: .99999 does not equal 1
« Reply #601 on: September 05, 2008, 09:21:42 AM »
There are infinite real numbers between any two numbers.

What about between i and √2[cos(π/4) + i sin(π/4)]?
I'm going to side with the white supremacists.

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Raist

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Re: .99999 does not equal 1
« Reply #602 on: September 05, 2008, 09:32:46 AM »
There are infinite real numbers between any two numbers.

What about between i and √2[cos(π/4) + i sin(π/4)]?
I is imaginary. I said real numbers.

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Parsifal

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Re: .99999 does not equal 1
« Reply #603 on: September 05, 2008, 09:34:11 AM »
I is imaginary. I said real numbers.

You said:

There are infinite real numbers between any two numbers.

Both of the numbers I gave were indeed numbers, and according to you should therefore have infinite real numbers between them.
I'm going to side with the white supremacists.

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zeroply

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Re: .99999 does not equal 1
« Reply #604 on: September 05, 2008, 09:51:10 AM »
The real number system, to the best of my knowledge, consists of all points that make up the number line. Since a line is continuous and infinite, the interval joining any two distinct points on it must be able to be bisected to give a number in between, and therefore any two distinct real numbers must have another real number between them.

Proof please. Not being facetious - ancients thought any point on the number line could be represented by a fraction. Obviously that doesn't work. Why are reals the magic number system that matches up with the number line?

There are infinite real numbers between any two numbers.

Proof please. I'll assume you mean real numbers. Again, this is not obvious. It certainly doesn't hold for hyperreals as I mentioned earlier.


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Raist

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Re: .99999 does not equal 1
« Reply #605 on: September 05, 2008, 09:52:22 AM »
I is imaginary. I said real numbers.

You said:

There are infinite real numbers between any two numbers.

Both of the numbers I gave were indeed numbers, and according to you should therefore have infinite real numbers between them.
You did get me there. I meant infinite real numbers between and two real numbers. Thanks for catching that. 9 am classes after drinking the night before.... Raist is not all the way here today.

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Trekky0623

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Re: .99999 does not equal 1
« Reply #606 on: September 05, 2008, 09:56:34 AM »
Imaginary numbers are assholes.

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Parsifal

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Re: .99999 does not equal 1
« Reply #607 on: September 05, 2008, 09:57:41 AM »
Proof please. Not being facetious - ancients thought any point on the number line could be represented by a fraction. Obviously that doesn't work. Why are reals the magic number system that matches up with the number line?

Isn't that how real numbers are defined?
I'm going to side with the white supremacists.

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zeroply

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Re: .99999 does not equal 1
« Reply #608 on: September 05, 2008, 10:16:32 AM »
Proof please. Not being facetious - ancients thought any point on the number line could be represented by a fraction. Obviously that doesn't work. Why are reals the magic number system that matches up with the number line?

Isn't that how real numbers are defined?

I've never seen a definition based on a number line. How would you go about labeling the points anyway? To the uninformed it might look like the rational numbers would be the logical outcome of labeling every point on the line, since I can generate as fine a ruler as I want just using fractions.

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Raist

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Re: .99999 does not equal 1
« Reply #609 on: September 05, 2008, 10:19:06 AM »
Proof please. Not being facetious - ancients thought any point on the number line could be represented by a fraction. Obviously that doesn't work. Why are reals the magic number system that matches up with the number line?

Isn't that how real numbers are defined?

I've never seen a definition based on a number line. How would you go about labeling the points anyway? To the uninformed it might look like the rational numbers would be the logical outcome of labeling every point on the line, since I can generate as fine a ruler as I want just using fractions.
Really? So you couldn't graph the point where Pi is located? You couldn't graph the point 1/3? Also you can label every single real number. And between every single real number is an infinite set of real numbers.

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Parsifal

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Re: .99999 does not equal 1
« Reply #610 on: September 05, 2008, 10:24:24 AM »
Really? So you couldn't graph the point where Pi is located? You couldn't graph the point 1/3? Also you can label every single real number. And between every single real number is an infinite set of real numbers.

1/3 is rational. Also, he does have a point: between any two rational numbers is an infinite set of rational numbers. That doesn't change the fact that 0.999... = 1, though, because the rationals are just a subset of the reals.
I'm going to side with the white supremacists.

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zeroply

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Re: .99999 does not equal 1
« Reply #611 on: September 05, 2008, 10:45:08 AM »
Really? So you couldn't graph the point where Pi is located? You couldn't graph the point 1/3? Also you can label every single real number. And between every single real number is an infinite set of real numbers.

1/3 is rational. Also, he does have a point: between any two rational numbers is an infinite set of rational numbers. That doesn't change the fact that 0.999... = 1, though, because the rationals are just a subset of the reals.

Easy rebuttal in so many other ways too - e.g. show me how you're going to graph the point 0.999... Remember, you can't have an infinite construction since it never ends. Otherwise I can show you how to graph infinity, which you would admit is not a real number.

How are you going to plot pi? Remember, you can't use analysis since that depends on having the foundation in place. I can see doing algebraic numbers, but transcendentals will be quite difficult. How about 1.12345678910111213141516...? If you can't plot that then I can claim it's not a real number.

Construction is everything. Under the Narcberry numbers construction (based on decimal expansions), 0.999... != 1

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Parsifal

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Re: .99999 does not equal 1
« Reply #612 on: September 05, 2008, 10:49:40 AM »
Easy rebuttal in so many other ways too - e.g. show me how you're going to graph the point 0.999... Remember, you can't have an infinite construction since it never ends. Otherwise I can show you how to graph infinity, which you would admit is not a real number.

It is not possible to graph infinity on an infinite number line.

How are you going to plot pi?

By rolling a unit circle exactly once to the right starting from zero.

How about 1.12345678910111213141516...? If you can't plot that then I can claim it's not a real number.

There's probably a way to plot it. I don't know what it is, though.
I'm going to side with the white supremacists.

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zeroply

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Re: .99999 does not equal 1
« Reply #613 on: September 05, 2008, 11:19:18 AM »
Easy rebuttal in so many other ways too - e.g. show me how you're going to graph the point 0.999... Remember, you can't have an infinite construction since it never ends. Otherwise I can show you how to graph infinity, which you would admit is not a real number.

It is not possible to graph infinity on an infinite number line.

That's my point. How are you going to graph 0.999... in a finite number of steps?

How are you going to plot pi?

By rolling a unit circle exactly once to the right starting from zero.

Doesn't work. You need to prove that a unit circle has the same number of points as a line. For all I know the unit circle only includes rational points. You need to do a compass and straightedge construction and I can tell you right now you won't be able to do it.

How about 1.12345678910111213141516...? If you can't plot that then I can claim it's not a real number.

There's probably a way to plot it. I don't know what it is, though.

You have to come up with a universal plotting system whereby if I give you any decimal expansion n1.d1d2d3... you can translate that into a point on the number line. Otherwise I can just say that some numbers can't be plotted, that 0.999... is one of those numbers, and therefore doesn't work the way you think it does as far as the rest of your claims based on the number line.

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Raist

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Re: .99999 does not equal 1
« Reply #614 on: September 05, 2008, 11:24:58 AM »
So you can graph 1/3 right?


can you graph .333333..... ?

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Parsifal

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Re: .99999 does not equal 1
« Reply #615 on: September 05, 2008, 11:26:39 AM »
You have to come up with a universal plotting system whereby if I give you any decimal expansion n1.d1d2d3... you can translate that into a point on the number line. Otherwise I can just say that some numbers can't be plotted, that 0.999... is one of those numbers, and therefore doesn't work the way you think it does as far as the rest of your claims based on the number line.

Hmm... that would be easy in binary, but I'm not sure if there's a way to quintisect an interval.
I'm going to side with the white supremacists.

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zeroply

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Re: .99999 does not equal 1
« Reply #616 on: September 05, 2008, 11:39:16 AM »
You have to come up with a universal plotting system whereby if I give you any decimal expansion n1.d1d2d3... you can translate that into a point on the number line. Otherwise I can just say that some numbers can't be plotted, that 0.999... is one of those numbers, and therefore doesn't work the way you think it does as far as the rest of your claims based on the number line.

Hmm... that would be easy in binary, but I'm not sure if there's a way to quintisect an interval.

You can convert the decimal sequence into a binary one without a foul since it's a clear bijective correspondence between the two sequences. I don't think that will help you any, because the construction sequence still has to be finite. Otherwise I can plot all sorts of interesting things that are not real numbers, such as positive infinity.

The best test case for your algorithm would be 0.12345678910111213141516... I didn't think that up though - it's called Champernowne's number if you want to look it up. It's a perfectly well defined real number so you should be able to plot it.

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zeroply

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Re: .99999 does not equal 1
« Reply #617 on: September 05, 2008, 11:43:16 AM »
As an aside, when you convert Champernowne's number into binary, you get a number that has every possible finite binary string embedded within it somewhere. If you digitized a picture of your grandmother and looked at the sequences of 1's and 0's, it is guaranteed to appear somewhere in the expansion. So does every poem, phone number, and work of Shakespeare.

Before anyone brings up the fact that pi behaves the same way, let me point out that no one has actually proved that yet.

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Parsifal

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Re: .99999 does not equal 1
« Reply #618 on: September 05, 2008, 11:43:31 AM »
You can convert the decimal sequence into a binary one without a foul since it's a clear bijective correspondence between the two sequences. I don't think that will help you any, because the construction sequence still has to be finite. Otherwise I can plot all sorts of interesting things that are not real numbers, such as positive infinity.

Ah, oops. The method I had in mind for binary would only work for non-repeating rational binary numbers.
« Last Edit: September 05, 2008, 11:45:28 AM by Osama bin Laden »
I'm going to side with the white supremacists.

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WardoggKC130FE

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Re: .99999 does not equal 1
« Reply #619 on: September 05, 2008, 11:50:05 AM »
18 pages...

0.99999 != 1
0.999...  = 1

[NOTE: THIS POST WILL BE SPAMMABLE SHOULD STUPIDITY CONTINUES BEYOND PAGE 18]

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zeroply

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Re: .99999 does not equal 1
« Reply #620 on: September 05, 2008, 11:58:15 AM »
18 pages...

0.99999 != 1
0.999...  = 1

[NOTE: THIS POST WILL BE SPAMMABLE SHOULD STUPIDITY CONTINUES BEYOND PAGE 18]

This is a legitimate argument. Unless you have some serious cred in analysis you're just trolling.

99% of the people out there who've taken calculus don't have a good grasp of the real numbers. I'm still waiting on a response as to how 0.999... = 1 if both are Narcberry numbers based on a decimal expansion definition.

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zeroply

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Re: .99999 does not equal 1
« Reply #621 on: September 05, 2008, 12:04:39 PM »
You can convert the decimal sequence into a binary one without a foul since it's a clear bijective correspondence between the two sequences. I don't think that will help you any, because the construction sequence still has to be finite. Otherwise I can plot all sorts of interesting things that are not real numbers, such as positive infinity.

Ah, oops. The method I had in mind for binary would only work for non-repeating rational binary numbers.

I think we can actually cover all algebraic numbers easily since we can deal with square roots and sums. The problem is when you hit the transcendentals - especially for non-normal numbers such as Champernowne's.

Re: .99999 does not equal 1
« Reply #622 on: September 05, 2008, 03:24:46 PM »
(1/3) / 3 = (1/9)

(1/3) + (1/9) = (4/9)

You fail.

it was in base 0.4 in a world in which 10 =1. I am winner

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narcberry

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Re: .99999 does not equal 1
« Reply #623 on: September 05, 2008, 04:42:44 PM »
Sorry folks, the longer you talk about it, the more obvious 0.999... cannot equal 1.

Re: .99999 does not equal 1
« Reply #624 on: September 05, 2008, 05:07:18 PM »
you can if you live in on flat earth, because pixies will let you. If you live in the real world then no

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narcberry

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Re: .99999 does not equal 1
« Reply #625 on: September 05, 2008, 05:17:34 PM »
Seriously RE'ers, when you start talking about pixies, you should probably leave the debate quietly.

Re: .99999 does not equal 1
« Reply #626 on: September 05, 2008, 05:19:34 PM »
why are we lumped together? we are all different, unless you are saying that all fes are the same..hmmm

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narcberry

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Re: .99999 does not equal 1
« Reply #627 on: September 05, 2008, 05:24:31 PM »
Maybe I shouldn't generalize. I meant:
When you start talking about pixies, you should probably leave the debate quietly.

This still means you.

Re: .99999 does not equal 1
« Reply #628 on: September 05, 2008, 05:25:12 PM »
why are we lumped together? we are all different, unless you are saying that all fes are the same..hmmm
Hey, we call them pixies, you call them gravitons...potato potatto...

Re: .99999 does not equal 1
« Reply #629 on: September 05, 2008, 05:26:48 PM »
fair enough. seems reasonable to me