Math Is Fun Forum

To John E. Franklin

Quote:
"A little off the subject, I just punched up this into my calculator:
1/.99 = 1.010101...
1/.999 = 1.001001001...
1/.9999 = 1.000100010001...
1/.99999... = 1.0000000000000000000000000000000000... So maybe you guys are right.
I guess it all depends if you can reason with the infinite."

ARB

Hi! The first Calculation is wrong!   1/0.9 = 1.11111111111............

The rest of my Proof! Speaks for itself!

Just to Back up a previous Post of Mine!

From the Cambridge Advanced Dictionary!

["Recurring number noun [C] (SPECIALIZED recurring decimal)
a number that repeats itself forever following a decimal point, such as 3.3333..."]

ARB

O.3333....is a number that repeats itself forever following a decimal point!
and so is..0.9999 ....a number that repeats itself forever following a decimal point

But I'm Quite Sure 1 is not! Especially as it has no Decimal point!!

Any thoughts on this!.....

Let's Just have a look at this! even though it's not the way I would describe Infinite 0.9

0.9999999999999999.........(recurring) = 1 ?

The problem with the Above is The Dictionary Definition of (recurring) is a Number that Repeats it's self!

If 0.9999999999999999.........(recurring) did = 1 then it would no Longer be Repeating  it's self ?

To Dross!

Your Little RUN! ended in the Last Post! on Another Post!

N1 = 0.9  “This is a Single Number Value”

and is the last Single Value then 0.2,0.3,0.4,0.5,0.6,0.7,0.8, Then N1 and Then 1

To Dross

Quote:"I seriously think you are getting confused between a number and a representation of a number. For example, pi has an infinite decimal expansion. I could start writing it out if I wanted to get accross what I mean, or I could simply write: Pi
One is an "infinitely long" representation of pi, the other is a succinct, explicit way of representing the same number.
So, I ask you, is 3.14... an "infinite number" (as you would say) even though it can be represented by a single charachter?

ARB

3.14...is an "infinite number" (as you would say) and it can be represented by a single charachter?
Give me one for a Single decimal Value that = One 3rd and I will use it!

None of this changes the fact that there are no Single decimal Values that = One 3rd

Which is where the Accuracy is Lost!

To Dross

Quote:"Unless you're trying to say that a "9" is the "last" digit in 0.9999... - when in fact there is no "last" digit since the digits never end."

A.R.B

N1 = 0.9  “This is a Single Number Value” And Yes! .9 is The Last Digit! Because its not an
Infinite Number the same as N2

Dross Quote:
"And in your second statement, you say that "there are an infinite amount of numbers between N2 and N3" - please note that having a number in your decimal expansion does not count as having that number "between" yourself and a larger number"

ARB
N4 is the Variable to Represent the .9,s which is Between N2  and N3
Because N4 is an Infinite number then Any amount of .9,s can be Inserted to Represent N4
Unless! " Anyone can Give! and Prove! a Value for N4 "

To Dross

Quote:"You are allowed to do that! 0.333... and 1/3 are two different representations of the same number! "

A.R.B:
It's not two different representations of the same number! or Numbers! We! are After! It,s Accuracy!

Unless you can Answer the Below! you have no case!

A = 0.3
B = 0.3
C = 0.3

A + B + C = 0.9

A = (Decimal Value)
B = (Decimal Value)
B = (Decimal Value)

Using the Three Decimal Values A + B + C above must equal 1

The Three Decimal Values must have the Same Values!

To Patric

Quote:

"And since A=B=C, they're all 0.333... or written as a fraction 1/3."

A.R.B

You are trying to mix Fractions! with Decimals Again!!

N1 = 0.9  “This is a Single Number Value”

N2 = Infinite 0.9  “This is an Infinite Number!”

N3 = 1  “This is a Single Number Value”

N4 = “The Maximum possible Number of .9's”

N1..............( N0 Numbers! )..........N3. 

N2..............( N4...Can have + .9's i.e More .9's )........N3.

First to Everyone!.......N1 is a Single Value i.e 0.9

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

I would now like to Add another Variable to this Example! N4

This is for anyone who feels it's not possible to place another Number between N2 and N3.

N4 = “The Maximum possible Number of .9's”

Anyone who feels it’s not possible to place another Number between N2 and N3, all they have to do to prove how they feel! Is giving a Value for N4.

So now we have!.....

N2..............( Here between N2 and N3 there are an Infinite Amount of Numbers! Because N2 is an
Endless stream of Numbers!).............N3. 

N2..............( How Ever! If..N4...is proved! Then the above is not True!).............N3. 

N2..............( But as it Stands!..N4...Can have + .9's i.e More .9's Between! Because N2 is Infinite!).............N3.

“If a Number has to be Infinitely Multiplied! To Try and Reach a Target Value! Then the Target Value! Must be Greater than the Number being Infinitely Multiplied! Reason Being! If the Target Value was also Infinitely Multiplied! Then the Target Value would again be Greater!
Number Infinitely Multiplied! = 0.9   Target Value! = 1 “

[Anthony.R.Brown 20/01/07].