0.9999....(recurring) = 1?

Ricky · 2007-03-08 18:55:31

George,Y wrote:

Ricky wrote:
George, I think we need to start from the basics. Let me know if you disagree with anything in this:
Let
Then A may be represented by the sequence:
Every term in this sequence can be labeled by an element in the natural numbers. As there is no infinity in the natural numbers, there is no "infiniteth" element.
No, don't try to hide your growing series or your counting into a bracket.

Sorry that you don't accept common set notation. How exactly does one write a set without brackets?

Sekky · 2007-03-08 23:49:11

Actually he has a point, you should be constructing a tuple, not a set.

Anthony.R.Brown · 2007-03-09 01:59:08

To Maelwys

Quote:

(1) " This proof has been countered many times, and you've still yet to raise a coherant defense for it. "

(2) " This quote has also been rebuttled above. "

(3) " I don't even understand this one... there's a 10% difference between what? 0 and 9? And where did the 1.8, 2.7, etc, come from? I'm thoroughly confused, sorry. "

A.R.B

you are joking of course!

(1) C <> ( C + D ) " INFINITE 0.9 <> 1 " " C must always = .999... and D must always = .001...

(C + D ) or A only = 1 " That's an Infinite Proof!! " making C < 1
........................................................................................................................................

(2) Prove yourself wrong with this one! and give us your Definition for Recurring?

(3) you will always be " thoroughly confused " unless you learn where Numbers come from! and how they are made!

Maelwys · 2007-03-09 02:29:27

Anthony.R.Brown wrote:

(1) C <> ( C + D ) " INFINITE 0.9 <> 1 " " C must always = .999... and D must always = .001...
(C + D ) or A only = 1 " That's an Infinite Proof!! " making C < 1

So your argument is that C MUST not be equal to C + D because 0.999... is not equal to 1, so C must be < 1, meaning that 0.999 is not equal to 1. The problem with this is still the second step... you're assuming 0.999... is not equal to 1, and using that to support your proof that it isn't. You can't just use an assumption to support a proof of that assumption, you must first prove it to be true. If you drop the assumption, then C can equal C + D for cases where D = 0, therefor C + D = 1 = A, if D = 0 then C = A.

Anthony.R.Brown wrote:

(2) " This quote has also been rebuttled above. "
(2) Prove yourself wrong with this one! and give us your Definition for Recurring?

Recurring - A recurring decimal (or "repeating decimal") is an expression representing a real number in the decimal numeral system, in which after some point the same sequence of digits repeats infinitely.

Anthony.R.Brown wrote:

(3) " I don't even understand this one... there's a 10% difference between what? 0 and 9? And where did the 1.8, 2.7, etc, come from? I'm thoroughly confused, sorry. "
(3) you will always be " thoroughly confused " unless you learn where Numbers come from! and how they are made!

Okay, I did some reading and learned that numbers originally come from Sumeria, between 8000 and 3500 BC. About 3100 BC they invented the concept of abstract numbers that don't represent specific items. Originally they were made of small clay tokens, but they gradually became markings made with a round stylus at different angles, to represent the different numbers.

Now although I find the history lesson fascinating, I'm sure that you didn't mean for me to study 10 000 years of numerical history to understand why you're multiplying 0.9 x 4 as part of a proof that shows there's a 10% difference between 3.6 and 4.0, which somehow represents that 0.999... is less than 1. But the problem is that I'm not sure what else you could mean by "where numbers come from and how they're made". Why does a number have to come from somewhere? Where does the number 1 come from? What about 0.9? What about 4? Does it matter where these numbers "come from"? We all understand what they represent, right? Or do we have to start this conversation with a proof of the relationship be 1 and 2, and why 3 <> 2, 3 > 2 > 1, and where does 4 fit into this odd series of symbols?

Ricky · 2007-03-09 06:12:31

Sekky wrote:

Actually he has a point, you should be constructing a tuple, not a set.

Honestly, I'm just trying to get the idea across of a countable set. I'm not going to get bogged down in specific math terms when the meaning is all I wish to convey. George doesn't seem to understand how you may have a set without an "infiniteth" element.

But yes, it should be a tuple and not a set.

Anthony.R.Brown · 2007-03-10 02:32:57

To Maelwys

Quote:

" Does it matter where these numbers "come from"? "

A.R.B

This is your Main Problem! as I said many times! Infinite/Recurring Numbers are not Plucked from the Sky!
you have to show the Math on how the Infinite/Recurring Numbers are made! so far you think they have no Start!
If you can show any Infinite/Recurring Number without a Start! you will be a Genius!!

Anthony.R.Brown · 2007-03-10 03:02:52

---------------------------------------------------------------------------------------------------------------
THE DEFINITIVE REASON INFINITE/RECURRING 0.9 IS < 1 AND <> 1 10/03/07
by Anthony.R.Brown
---------------------------------------------------------------------------------------------------------------

( 1 ) If any Number Starts or has a Zero followed by a Decimal point at the beginning! it will always be < 1 and <> 1 if no additional Math is applied to the Number!

( 2 ) Numbers that conform to ( 1 ) as examples are 0.1 to 0.9

( 3 ) Infinite/Recurring Numbers have no end! the Numbers repeat themselves endlessly!

( 4 ) Because Infinite/Recurring Numbers are always the same Number being repeated,we don't need to try and write down many as examples,because the Number is always the same.

( 5 ) An example for ( 4 ) is Infinite/Recurring ( 0.9 ) = 0.9 the reason this is True is because the Number never changes!

( 6 ) The same can be applied to any Infinite/Recurring ( N ) = N

( 7 ) From ( 5 ) and ( 6 ) we can prove Infinite/Recurring ( 0. 1 ) to ( 0.9 ) < 1 and <> 1

1 - ( 0.1 ) = 0.9 and <> 1
1 - ( 0.2 ) = 0.8 and <> 1
1 - ( 0.3 ) = 0.7 and <> 1
1 - ( 0.4 ) = 0.6 and <> 1
1 - ( 0.5 ) = 0.5 and <> 1
1 - ( 0.6 ) = 0.4 and <> 1
1 - ( 0.7 ) = 0.3 and <> 1
1 - ( 0.8 ) = 0.2 and <> 1
1 - ( 0.9 ) = 0.1 and <> 1

---------------------------------------------------------------------------------------------------------------

Last edited by Anthony.R.Brown (2007-03-10 03:05:37)

Sekky · 2007-03-10 04:51:23

( 1 ) If any Number Starts or has a Zero followed by a Decimal point at the beginning! it will always be < 1 and <> 1 if no additional Math is applied to the Number!

Wrong, any terminating rational expression has two real valued decimal expansions.

Edit: From Wikipedia's 0.999 page: "every non-zero, terminating decimal has a twin with trailing 9s".

The numbers are identical, please go and study something you can't break, like a manhole cover subject like sociology.

Last edited by Sekky (2007-03-10 04:54:12)

Anthony.R.Brown · 2007-03-11 00:44:43

To Sekky

Quote:

" Wrong, any terminating rational expression has two real valued decimal expansions "

A.R.B

an expression! such as INFINITE/RECURRING 0.9 can only have one Value! if there were

" two real valued decimal expansions ? " then there would be a Contradiction!!

Anthony.R.Brown · 2007-03-11 00:51:31

---------------------------------------------------------------------------------------------------------------
THE INFINITE/RECURRING ( N ) = N PROOF 11/03/07 by Anthony.R.Brown
---------------------------------------------------------------------------------------------------------------

Infinite Recurring ( n ) = n because! ( n ) will always = n

Maelwys · 2007-03-11 00:56:33

Anthony.R.Brown wrote:

---------------------------------------------------------------------------------------------------------------
THE INFINITE/RECURRING ( N ) = N PROOF 11/03/07 by Anthony.R.Brown
---------------------------------------------------------------------------------------------------------------
Infinite Recurring ( n ) = n because! ( n ) will always = n

Wow, that's so wrong....
So 0.222... = 2?

I'll assume you mean 0.222 = 0.2; But that's wrong too
0.555... = 0.5? What about the 0.0555... difference?

Anthony.R.Brown · 2007-03-11 00:59:27

To Maelwys

Quote: " Wow, that's so wrong.... So 0.222... = 2? "

A.R.B

How is it!! everything you read!? you dont understand!!

Infinite Recurring ( 0.2 ) = 0.2 because! (0.2 ) will always = 0.2

Maelwys · 2007-03-11 00:59:38

Instead of just countering points, I'll try posting one of my own for Anthony to counter.
If 0.999... is 0.000...1 difference from 1, where 0.000...1 has an infinite amount of 0s, followed by(?) a 1, then what is half of the value of 0.000...1? For any two numbers that are not equal, we should be able to find the average of those two numbers, being equal to half the difference between them. So the average of 0.999... and 1 should be equal to 0.999... + (0.000...1 / 2), so I'm wondering how you believe we'd be able to do that math, and what the answer should be?

Sekky · 2007-03-11 01:04:17

Anthony.R.Brown wrote:

To Sekky
Quote:
" Wrong, any terminating rational expression has two real valued decimal expansions "
A.R.B
an expression! such as INFINITE/RECURRING 0.9 can only have one Value! if there were
" two real valued decimal expansions ? " then there would be a Contradiction!!

They are the same value, with two real value decimal expansions.

I have a challenge for anybody reading this thread, find me somebody worse at maths than this guy.

Anthony.R.Brown · 2007-03-11 01:07:16

To Sekky

Quot:

" They are the same value, with two real value decimal expansions. "

A.R.B

can you give us the same value? with two real value decimal expansions.?

Sekky · 2007-03-11 01:09:10

Anthony.R.Brown wrote:

can you give us the same value? with two real value decimal expansions.?

...so give them both different names, they'll still be the same value

call them "stupid" and "moron", accept that they have the same numerical value, and how you write them in text doesn't make a blind bit of different to how you use them in practise.

Maelwys · 2007-03-11 01:11:29

Anthony.R.Brown wrote:

To Maelwys
Quote: " Wow, that's so wrong.... So 0.222... = 2? "
A.R.B
How is it!! everything you read!? you dont understand!!
Infinite Recurring ( 0.2 ) = 0.2 because! (0.2 ) will always = 0.2

I was just reading your answer the way it was written, because it's not the 0.2 that's recurring, it's just the 2, so it should be written as 0.222... = 0.(2), not (0.2).

Anyway, I correctly assumed what you'd really meant in the next line of my post, and then explained why that was wrong too... which you apparantly ignored.

Anthony.R.Brown · 2007-03-11 01:12:03

To Sekky

Quote: " ...so give them both different names, they'll still be the same value

call them "stupid" and "moron", accept that they have the same numerical value, and how you write them in text doesn't make a blind bit of different to how you use them in practise. "

A.R.B

so just SHUT you up in one big swoop!

you will find! they must both equal! Infinite Recurring ( n ) = n because! ( n ) will always = n

Maelwys · 2007-03-11 01:13:30

Sekky wrote:

Anthony.R.Brown wrote:
To Sekky
Quote:
" Wrong, any terminating rational expression has two real valued decimal expansions "
A.R.B
an expression! such as INFINITE/RECURRING 0.9 can only have one Value! if there were
" two real valued decimal expansions ? " then there would be a Contradiction!!
They are the same value, with two real value decimal expansions.
I have a challenge for anybody reading this thread, find me somebody worse at maths than this guy.

Well, my 7 month old son is sitting on my lap right now... he doesn't seem to understand the thread either, if that helps. ;-)

Maelwys · 2007-03-11 01:14:30

Anthony.R.Brown wrote:

To Sekky
Quote: " ...so give them both different names, they'll still be the same value
call them "stupid" and "moron", accept that they have the same numerical value, and how you write them in text doesn't make a blind bit of different to how you use them in practise. "
A.R.B
so just SHUT you up in one big swoop!
you will find! they must both equal! Infinite Recurring ( n ) = n because! ( n ) will always = n

You do realize that your "proof" is the same as saying:
2 = 1 because 2 will always equal 1
Right?

Anthony.R.Brown · 2007-03-11 01:15:55

To Maelwys

Quote: " I was just reading your answer the way it was written, because it's not the 0.2 that's recurring, it's just the 2, so it should be written as 0.222... = 0.(2), not (0.2). "

A.R.B

we are only talking about Infinite Recurring ( 0.2 ) the 0.2 Value is endless! so must always have the same Value!

Maelwys · 2007-03-11 01:16:49

Sekky wrote:

( 1 ) If any Number Starts or has a Zero followed by a Decimal point at the beginning! it will always be < 1 and <> 1 if no additional Math is applied to the Number!
Wrong, any terminating rational expression has two real valued decimal expansions.
Edit: From Wikipedia's 0.999 page: "every non-zero, terminating decimal has a twin with trailing 9s".
The numbers are identical, please go and study something you can't break, like a manhole cover subject like sociology.

Unfortunately, although you're correct, this isn't a valid proof. As I've been trying to show ARB, you can't prove something by assuming that it's true and then applying that assumption. We're trying to prove the validity of that statement made by Wikipedia, so we can't use the statement itself as a proof of itself.

And ARB:
What that entry is saying is that for any number, you can make several decimal expansions that look different, but are equal.
So 1.5 = 1.5000... = 1.4999..., all the same value. You can do the same thing for any number.

Sekky · 2007-03-11 01:19:22

Anthony.R.Brown wrote:

To Sekky
so just SHUT you up in one big swoop!
you will find! they must both equal! Infinite Recurring ( n ) = n because! ( n ) will always = n

Circular and fallacious

Just what exactly do you hope to gain by kidding yourself into thinking you're right? Or do you actually believe you're some enlightened high school child who understands everything on a level nobody else does? Get a clue, you haven't discovered something profound, in fact, you have to take at least an extra few steps to catch up with the rest of the muppets your age. It is YOUR logic that is backwards, and it is YOU that needs to start thinking. We can see your logic fails from outside it, you can't see it fails because you're stuck inside it and your little brain can't comprehend that it's circular.

Anthony.R.Brown · 2007-03-11 01:25:11

To Maelwys

Quote: " 1.5000... = 1.4999... "

A.R.B

1.5000... - 1.4999... = 0.0001 this is an Infinite Calculation! and can be proved the same Difference exists! no matter how many decimal places you want to try!

Example A = Infinite ( 1.50 ) B = Infinite ( 1.49 ) A - B = 0.001...

Anthony.R.Brown · 2007-03-11 01:27:49

To Sekky

A.R.B

when the apple falls on your head! you may wake up!! but untill then! take notes from someone who knows more then you!

Math Is Fun Forum

#576 2007-03-08 18:55:31

Re: 0.9999....(recurring) = 1?

#577 2007-03-08 23:49:11

Re: 0.9999....(recurring) = 1?

#578 2007-03-09 01:59:08

Re: 0.9999....(recurring) = 1?

#579 2007-03-09 02:29:27

Re: 0.9999....(recurring) = 1?

#580 2007-03-09 06:12:31

Re: 0.9999....(recurring) = 1?

#581 2007-03-10 02:32:57

Re: 0.9999....(recurring) = 1?

#582 2007-03-10 03:02:52

Re: 0.9999....(recurring) = 1?

#583 2007-03-10 04:51:23

Re: 0.9999....(recurring) = 1?

#584 2007-03-11 00:44:43

Re: 0.9999....(recurring) = 1?

#585 2007-03-11 00:51:31

Re: 0.9999....(recurring) = 1?

#586 2007-03-11 00:56:33

Re: 0.9999....(recurring) = 1?

#587 2007-03-11 00:59:27

Re: 0.9999....(recurring) = 1?

#588 2007-03-11 00:59:38

Re: 0.9999....(recurring) = 1?

#589 2007-03-11 01:04:17

Re: 0.9999....(recurring) = 1?

#590 2007-03-11 01:07:16

Re: 0.9999....(recurring) = 1?

#591 2007-03-11 01:09:10

Re: 0.9999....(recurring) = 1?

#592 2007-03-11 01:11:29

Re: 0.9999....(recurring) = 1?

#593 2007-03-11 01:12:03

Re: 0.9999....(recurring) = 1?

#594 2007-03-11 01:13:30

Re: 0.9999....(recurring) = 1?

#595 2007-03-11 01:14:30

Re: 0.9999....(recurring) = 1?

#596 2007-03-11 01:15:55

Re: 0.9999....(recurring) = 1?

#597 2007-03-11 01:16:49

Re: 0.9999....(recurring) = 1?

#598 2007-03-11 01:19:22

Re: 0.9999....(recurring) = 1?

#599 2007-03-11 01:25:11

Re: 0.9999....(recurring) = 1?

#600 2007-03-11 01:27:49

Re: 0.9999....(recurring) = 1?

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