0.9999....(recurring) = 1?

Ninja 101 · 2007-06-14 01:58:10

It's all kinda difficult to get your head around.

luca-deltodesco · 2007-06-14 02:10:23

whats your point with the 1/0.3 and 1/0.33 what are you trying to show here?

and yes, 0.3 IS the same as 0.3000... they are exacttly the same.

Maelwys · 2007-06-14 02:14:19

Anthony.R.Brown wrote:

1 / 0.3 = 0.333...
1 / 0.33 = 0.030...
And not 0.3 is the same as 0.3000....,

0.3 IS the same as 0.3000... though. I'm not sure what the above two calculations are supposed to prove, really.

Do you want more examples of averaging infinitely repeating numbers? I can even find the average of a repeating number with a non-repeating number. For example the average of 0.444... and 1 is 0.722(2)... The average of 1.232323(23)... and 5 is 3.0909(09).... The average of 1.5353(53)... and 2.361361(361)... is 1.9483574483574(483574)...

The moral of the story is that any two real numbers that have different values, also have a third real number with a unique value that is halfway between them, that represents the average of those two numbers. But for 1 and 0.999... there is no such value, which means that either 0.999... isn't a real number, or 0.999... has the same value as 1.

Anthony.R.Brown · 2007-06-15 00:59:49

So Back to the Impossible Question!

If you can Show how to Average an Unknown Number/Value Concerning Length and/or Decimal Places!

Its no Good just saying The average of Something is! "As far as Math goes! we need to know the Value as in Decimal Places! "

Otherwise we can of Course Average anything no Math needed!
Example! Average Elephant and Elephant = Elephant

Now for the the Wise Guys!
give us a Math Value (Decimal Places) for 1 and Infinite/Recurring 0.9

A.R.B

Maelwys · 2007-06-15 01:09:06

Anthony.R.Brown wrote:

If you can Show how to Average an Unknown Number/Value Concerning Length and/or Decimal Places!
Its no Good just saying The average of Something is! "As far as Math goes! we need to know the Value as in Decimal Places! "

Did you even read my post, with lots of examples of how it IS possible to calculate the averages?
And remember, we're not dealing with unknown numbers here at all. We're dealing with infinitely long repeating decimals. Infinite doesn't mean "we don't know how many numbers follow because we can't count that high", it means "there's more numbers here than the largest finite (real or natural) number". You seem to be insisting on treating the "..." as "some more numbers follow, we don't know how many". If that was the case then yes, all of your arguments would be correct. There would indeed be a number that could add to 0.999(x more 9s) with a value of 0.000(x-1 more 0s)1 to make it equal 1. Though you'd still be able to calculate an average of 0.999(x more 9s)5 for it, but that's not a real number until we know the value of x. But the ... isn't an unknown variable, it's an unending number. There's definitely a difference here.

Anthony.R.Brown · 2007-06-15 01:09:49

Now for the the Wise Guys!
give us a Math Value (Decimal Places) for 1 and Infinite/Recurring 0.9

A.R.B

Maelwys · 2007-06-15 01:11:42

Anthony.R.Brown wrote:

Now for the the Wise Guys!
give us a Math Value (Decimal Places) for 1 and Infinite/Recurring 0.9

I'm not sure I undestand the question. You want to know how many digits follow the decimal place in each of those numbers? Well, 1 can have either 0 digits after the decimal (1) or infinite digits (1.000...). And 0.999... has infinite digits.

Anthony.R.Brown · 2007-06-15 01:16:51

1 / 2 = 0.5

Infinite/Recurring 0.9 / 2 = ?

Maelwys · 2007-06-15 01:19:21

Anthony.R.Brown wrote:

1 / 2 = 0.5
Infinite/Recurring 0.9 / 2 = ?

0.999... / 2 = 0.5, because 0.999... = 1. ;-)
Or if you prefer
0.999... / 2 = 0.4999... (which incidentally, also = 0.5)

Anthony.R.Brown · 2007-06-15 01:27:46

To Maelwys

Quote:" 0.999... / 2 = 0.5, because 0.999... = 1. ;-)
Or if you prefer
0.999... / 2 = 0.4999... (which incidentally, also = 0.5) "

A.R.B

Wrong!!

0.9 / 2 " 1 Decimal Place " = 0.45

0.99 / 2 " 2 Decimal Place " = 0.495

0.9 Infinite Decimal Places / 2 " True Value can never be Calculated! "

0.4999... <> 0.5

Maelwys · 2007-06-15 01:40:41

Anthony.R.Brown wrote:

To Maelwys
Quote:" 0.999... / 2 = 0.5, because 0.999... = 1. ;-)
Or if you prefer
0.999... / 2 = 0.4999... (which incidentally, also = 0.5) "
A.R.B
Wrong!!
0.9 / 2 " 1 Decimal Place " = 0.45
0.99 / 2 " 2 Decimal Place " = 0.495
0.9 Infinite Decimal Places / 2 " True Value can never be Calculated! "
0.4999... <> 0.5

Now you're just starting the exact same argument all over again with slightly different numbers. I understand that you refuse to believe that 0.999... = 1, and as such don't believe that 0.4999... = 0.5, nor 6.34999... = 6.35, but I don't think we need to argue every single case.

You still never answered my above question about the average of 0.999... and 1. If 0.999... is a real number < 1, then there must be another real number existing (x) where 0.999... < x < 1. The easiest such x to find should be simply the average of the two numbers that it's between. So what is that average? What is that number that exists between 0.999... and 1?

Or would you rather assert that 0.999... isn't a real number at all? That's something that you might at least make a case for. But if that's your case then you have to drop this nonsense that 1 - 0.999... = 0.000...1, because 0.000...1 isn't a real number either, and if we're starting to play with non-real numbers than we can't actually calculate anything because most of the normal rules of math cease to apply.

Anthony.R.Brown · 2007-06-15 01:44:04

To Maelwys

Quote:" You still never answered my above question about the average of 0.999... and 1. If 0.999... is a real number < 1, then there must be another real number existing (x) where 0.999... < x < 1. The easiest such x to find should be simply the average of the two numbers that it's between. So what is that average? What is that number that exists between 0.999... and 1? "

A.R.B

There is only More 0.9's Between Infinite/Recurring 0.9 and 1

All you have to accept! is that there are Numbers Infinitely < 1

Last edited by Anthony.R.Brown (2007-06-15 01:52:59)

Maelwys · 2007-06-15 01:47:20

Anthony.R.Brown wrote:

There is only More 0.9's Between Infinite/Recurring 0.9 and 1
All you have to accept! is that there are Numbers Infinitly < 1

Can you show us one of these "more 0.9s" numbers?
0.999... has an infinite number of 9s. So you're asserting that there's another number bigger than 0.999... but less than 1, that has more than an infinite number of 9s? So to count from 0.999... to 1 ...
0.999... (infinite 9s)
0.999... (infinite +1 9s)
0.999... (infinite +2 9s)
...
0.999... (infinite + infinite 9s)
0.999... (2x infinite +1 9s)
0.999... (2x infinite +2 9s)
...
(etc, etc, etc)

Is this correct?

Anthony.R.Brown · 2007-06-15 02:00:14

Infinite 0.9 ( Stage One Decimal Place ) = 0.9

Infinite 0.9 ( Stage One Decimal Place ) + ( The Next Decimal Place " More 0.9's ) = 0.99

Infinite 0.9 ( Stage Infinite Decimal Place's ) = " More 0.9's " As always Before 1

Maelwys · 2007-06-15 02:05:18

Anthony.R.Brown wrote:

Infinite 0.9 ( Stage One Decimal Place ) = 0.9
Infinite 0.9 ( Stage One Decimal Place ) + ( The Next Decimal Place " More 0.9's ) = 0.99
Infinite 0.9 ( Stage Infinite Decimal Place's ) = " More 0.9's " As always Before 1

But what number is halfway between "Infinite 0.9 (Stage Infinite Decimal Place's)" and 1?

Anthony.R.Brown · 2007-06-15 02:08:39

To Maelwys

Quote:" But what number is halfway between "Infinite 0.9 (Stage Infinite Decimal Place's)" and 1? "

A.R.B

There is no Halfway! Concerning Infinity! But from Infinite/Recurring 0.9 ( Stage 0ne Decimal Place ) There will always be More 0.9's

Maelwys · 2007-06-15 02:12:55

Anthony.R.Brown wrote:

There is no Halfway! Concerning Infinity! But from Infinite/Recurring 0.9 ( Stage 0ne Decimal Place ) There will always be More 0.9's

So your argument is that 0.999... isn't a real number, then? Like I said above, this argument at least might have half a leg to stand on. Though then we can't prove any of the properties of this "number" using math, because normal math rules only apply to real numbers or complex numbers, and this doesn't seem to be either. So it's now basically just a digital representation of your ideal for a value less than (but almost equal to) 1. But still not a number, by conventional definitions of such.

Of course if you want to start arguing whether or not 0.999... is a real number then we'll just have to start from scratch with an entirely new set of arguments, and I can probably argue against that too... just saying... ;-)

Anthony.R.Brown · 2007-06-15 02:26:06

To Maelwys

Quot:" So your argument is that 0.999... isn't a real number, then? Like I said above, this argument at least might have half a leg to stand on. "

A.R.B

Infinte/Recurring 0.9 is a Number/Value But not a Fixed Number/Value! as with Whole Numbers!

Infinite/Recurring 0.9 = 0.(n) < 1 The 0.(n) is the Value from 1 - Infinite/Recurring 0.9 = 0.001...

So we can have 0.999... and 0.001... Where 0.999... + 0.001... = 1

luca-deltodesco · 2007-06-15 02:29:44

there is no such thing as a number that has a non static-value, otherwise its a variable, not a number.

Maelwys · 2007-06-15 02:33:05

Anthony.R.Brown wrote:

Infinte/Recurring 0.9 is a Number/Value But not a Fixed Number/Value! as with Whole Numbers!
Infinite/Recurring 0.9 = 0.(n) < 1 The 0.(n) is the Value from 1 - Infinite/Recurring 0.9 = 0.001...
So we can have 0.999... and 0.001... Where 0.999... + 0.001... = 1

I like how you always manage to completely avoid actually giving an answer to any direct question you're asked. Instead you just put a cut/paste of some irrelevant point you'd made 3 pages ago and leave it up to us to attempt to interpret how your "answer" has any impact on the question asked, and from there to guess at what it means you believe in relation to the actual question that was put forward.

In this case, I'm going to interpret the above to mean that you do indeed claim 0.999... isn't a real number. Unfortunately that interpretation leaves the rest of your post irrelevant, since we can't argue over what math does or doesn't make sense to perform on an unreal number, since no rules exist for that. So lacking any rules or any form of system to define what can and can't be done with an unreal number... hell, we're even lacking anything to call a "number" that's neither real nor complex... I'm forced to agree that whatever you put down there must make sense, since only you understand the "system" that you've apparently invented to deal with this peculiar case of an unreal number.

Or in other words:
0.6TG12bunnyrabbit + 63.523$omega23 = 2
Because in my system of unreal numbers that I choose to refer to as "hobos", I say so.

;-)

Anthony.R.Brown · 2007-06-15 02:36:19

To luca-deltodesco

Quote:" there is no such thing as a number that has a non static-value, otherwise its a variable, not a number "

A.R.B

I Said Number/Value! " Knowing we are Talking about Infinity! is the point! "

luca-deltodesco · 2007-06-15 02:58:14

find then, there is no such thing as a number/value that has a non static-value, otherwise its a variable, not a number/value

Anthony.R.Brown · 2007-06-16 02:42:37

To luca-deltodesco

Quote:" find then, there is no such thing as a number/value that has a non static-value, otherwise its a variable, not a number/value "

A.R.B

Next you will be Saying Infinite/Recurring Number/Values are Integer Whole Number/Values!

Anthony.R.Brown · 2007-06-16 03:01:01

Infinite/Recurring Number/Values!

Depending on how Many Decimal Places are Calculated! The Static Value Changes!

Infinite/Recurring 0.9 ( One Decimal Place ) 0.9 has a Different Static Value To ........................

Infinite/Recurring 0.9 ( Two Decimal Place's ) 0.99 ...............................................................

Last edited by Anthony.R.Brown (2007-06-16 03:02:13)

Anthony.R.Brown · 2007-10-16 07:33:15

-------------------------------------------------------------------------------------------------------------------------------------------------------
HOW TO CALCULATE AND UNDERSTAND INFINITE/RECURRING NUMBER/VALUES By Anthony.R.Brown 16/10/07.
-------------------------------------------------------------------------------------------------------------------------------------------------------

First of all it is important to give and use Variables that are clear and easy to identify for what they stand for,the Variables below should be easy to follow.

N = 0.9 " This is the start Value used for Infinite/Recurring 0.9 there has to be one! it did not come from thin Air!..."

O = 1 " This is the Integer whole Number One! "

I = 1.111..." This is the Infinite Calculation! that is used from the Formula ( 1 / 0.9 ) x ( 0.9 ) = ( 1.111...)

R = " The Result Variable! "

So we now have Only four Variables! N,O,I,R that are Clear to spot and use! as examples...It is Only nesessary to use these four variables to Show how to Calculate Infinite/Recurring Number/Values! So Only use them!...

Below is my Formula to Calculate Infinite/Recurring 0.9 in Numbers Only form! and the same Formula using the Variables above!...

Numbers ( 1 / 0.9 ) = ( 1.111...) x ( 0.9 ) = 0.999... And now the Variables ( O / N ) = ( I ) x ( N ) = ( R ) " Which also equals 0.999..."

What can be seen clearly from my Formula above by using the Variables is! that at no time are any of the .9s being Rounded up in any way by using the Classic Math trick ( 0.9 / 0.9 ) = 1 there is Only one ( N ) Value and Only one ( R ) Value! both are Different!...

Examples below must not be used to make Any two Numbers that are the same equal 1

N / N = 1 " But this does not make the Original Value for N = 1 "

O / O = 1 " But this does not make the Original Value for O = 1 it already is! "

I / I = 1 " But this does not make the Original Value for I = 1 "

R / R = 1 " But this does not make the Original Value for R = 1 "

Now let´s look at some other Mistakes people are making when Calculating Infinite/Recurring Number/Values!

I have seen the Calculation Infinite/Recurring 0.9 equals " 0.9 + 9 + 9 + 9 ...etc. "
where the .9´s are shown as being connected! with the first .9 as though it is a continuous Calculation being Add! this is a serious mistake and where there is a lot of confusion!
The true Value for Infinite/Recurring 0.9 is where the first .9 is being Infinitely repeated Over and Over again! so that the Calculation actually never moves away from being any Greater than 0.9 there may be many .9´s but they are Repetitions of the first! not being Add!
The True way to show Infinite/Recurring 0.9 should be with the .9´s Seperated! as here Infinite/Recurring 0.9 = .9,.9,.9,...etc. where each .9 has the Original value equal to 0.9

The Result will always be 1 - 0.9 = 0.1 where 0.1 is the Infinite/Recurring 0.1 Difference!...

Anthony.R.Brown 16/10/07.

Math Is Fun Forum

#801 2007-06-14 01:58:10

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

#802 2007-06-14 02:10:23

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

#803 2007-06-14 02:14:19

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

#804 2007-06-15 00:59:49

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

#805 2007-06-15 01:09:06

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

#806 2007-06-15 01:09:49

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

#807 2007-06-15 01:11:42

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

#808 2007-06-15 01:16:51

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

#809 2007-06-15 01:19:21

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

#810 2007-06-15 01:27:46

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

#811 2007-06-15 01:40:41

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

#812 2007-06-15 01:44:04

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

#813 2007-06-15 01:47:20

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

#814 2007-06-15 02:00:14

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

#815 2007-06-15 02:05:18

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

#816 2007-06-15 02:08:39

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

#817 2007-06-15 02:12:55

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

#818 2007-06-15 02:26:06

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

#819 2007-06-15 02:29:44

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

#820 2007-06-15 02:33:05

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

#821 2007-06-15 02:36:19

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

#822 2007-06-15 02:58:14

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

#823 2007-06-16 02:42:37

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

#824 2007-06-16 03:01:01

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

#825 2007-10-16 07:33:15

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

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