0.9999....(recurring) = 1?

mikau · 2007-05-26 17:43:54

Ricky wrote:

mikau, it's valid, but there are much easier ways to evaluate the sum, such as geometric series.

Okay, so what are we trying to show now?

Anthony.R.Brown · 2007-05-27 02:21:05

To mikau

Post 08:00:32 Quote:" hey guys, I posted this in a 0.999... thread in the Euler Avenue forum, but it looks like this is more the official thread for this topic. So I'm moving it here.

What do you think of this proof?

A.R.B

Still cant see how you have got Rid of the Infinite/Recurring 0.001... Difference!......................
as in 1 - Infinite/Recurring 0.999...

Last edited by Anthony.R.Brown (2007-05-27 02:22:44)

Maelwys · 2007-05-27 02:27:28

Anthony.R.Brown wrote:

To mikau
Post 08:00:32 Quote:" hey guys, I posted this in a 0.999... thread in the Euler Avenue forum, but it looks like this is more the official thread for this topic. So I'm moving it here.
What do you think of this proof?
A.R.B
Still cant see how you have got Rid of the Infinite/Recurring 0.001... Difference!......................
as in 1 - Infinite/Recurring 0.999...

That's the point. He didn't have to get rid of it. He started with one statement, and proved that it was equal to another statement. If that difference had been there, he wouldn't have been able to prove that without getting rid of the difference. But because he didn't have to get rid of the difference, obviously there was no difference there at all. That's how a proof works.

Anthony.R.Brown · 2007-05-27 02:46:22

To Maelwys

Quote:" That's the point. He didn't have to get rid of it. He started with one statement, and proved that it was equal to another statement. If that difference had been there, he wouldn't have been able to prove that without getting rid of the difference. But because he didn't have to get rid of the difference, obviously there was no difference there at all. That's how a proof works."

A.R.B

Exactly he started with the assumption that it was not there! that is the flaw!

We all know by now! that Infinite/Recurring 0.9 starts 0.1 less than 1 otherwise it would be called 1 to start with!

Infinite 1.111... x 0.9 will always have the .1 missing..............

Maelwys · 2007-05-27 03:00:15

Anthony.R.Brown wrote:

To Maelwys
Quote:" That's the point. He didn't have to get rid of it. He started with one statement, and proved that it was equal to another statement. If that difference had been there, he wouldn't have been able to prove that without getting rid of the difference. But because he didn't have to get rid of the difference, obviously there was no difference there at all. That's how a proof works."
A.R.B
Exactly he started with the assumption that it was not there! that is the flaw!
We all know by now! that Infinite/Recurring 0.9 starts 0.1 less than 1 otherwise it would be called 1 to start with!
Infinite 1.111... x 0.9 will always have the .1 missing..............

No, he didn't start with any assumption. He started with a number, manipulated it a bit, and came to a conclusion, without ever assuming that the number at the start was or wasn't equal to 1.

You're trying to enforce the assumption that there is a difference there.

Sekky · 2007-05-27 08:11:46

Anthony.R.Brown wrote:

Infinite 1.111... x 0.9 will always have the .1 missing..............

Whatever this means, it isn't true.

Anthony.R.Brown · 2007-05-29 00:18:43

Quote:" Whatever this means, it isn't true. "

Infinite 1.111... x 0.9 will always have the .1 missing............

A.R.B

Prove it wrong!.....................................................................................................................

Anthony.R.Brown · 2007-05-29 00:20:00

I thought I would copy these here! as it's the Post most Suited!

Below is a program wrote in the Basic Computer Language! that does exactly what it is asked! i.e Calculate Infinite/Recurring 0.9 with no end! ever!................

10 N = 0.9
20 INPUT " PRESS ENTER " ; START
30 PRINT ; N
40 GOTO 10

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

Below is my Infinite/Recurring 0.9 QBASIC Computer program!

To Run the program copy/paste and then save the file as INFREC09.BAS or INFREC09.TXT
then open the program in the QBASIC program's window to Run.

If you dont have a copy of the QBASIC program,it can be download for Free from

http://members.lycos.co.uk/brisray/qbasic/qind.htm

REM ************************************************************************
DIM TIMES AS SINGLE
DIM DECIMALPOINT AS STRING
DIM NINE AS STRING
DIM COUNT AS SINGLE
DIM RUNAGAIN AS STRING
CLS
PRINT
PRINT " INFINITE/RECURRING 0.9 QBASIC PROGRAM,By Anthony.R.Brown 17/05/07 "
PRINT
INPUT " ENTER HOW MANY TIMES TO RUN! THEN PRESS < ENTER > "; TIMES
PRINT : PRINT
DECIMALPOINT = "."
NINE = "9"
PRINT ; DECIMALPOINT;
NINES:
PRINT ; NINE;
COUNT = COUNT + 1
IF COUNT = TIMES THEN GOTO ENDOFRUN
GOTO NINES
ENDOFRUN:
PRINT : PRINT
PRINT " THE PROGRAM WILL RUN AN INFINITE/RECURRING AMOUNT OF TIMES! "
PRINT " IF YOU JUST PRESS < ENTER > FOR HOW MANY TIMES TO RUN! "
PRINT : PRINT
INPUT " PRESS < ENTER > TO RUN AGAIN "; RUNAGAIN
PRINT : PRINT
RUN
END
REM ************************************************************************

mathsyperson · 2007-05-29 01:07:21

As far as I can tell, that's not even calculating anything. You're just telling it to write 0. and then 9 lots of times.

Anthony.R.Brown · 2007-05-29 01:24:52

To mathsyperson

Quote:" As far as I can tell, that's not even calculating anything. You're just telling it to write 0. and then 9 lots of times. "

A.R.B

It must be doing the same trick other programs use! to prove Infinite/Recurring 0.9 = 1
ie. Mathmatica6 because how else can you get from 0.999...(9) to 1 without cheating!

So far no one on this site who thinks Infinite/Recurring 0.9 = 1 has ever shown the Math! or as you have asked about the Calculations!!...........

mikau · 2007-05-29 05:22:41

Below is my Infinite/Recurring 0.9 QBASIC Computer program!

did you just say infinite recurruring computer program?

Thats offensive.

Last edited by mikau (2007-05-29 05:43:11)

mikau · 2007-05-29 12:15:04

Anthony, I'm not sure what your argument is. Are you trying to say that 0.9999... is not equal to 1 becuase if you write a program to print a lengthy stream of 9's, it doesn't magically transform itself into the digit 1? This is supposed to be proof that it isn't true?

First off, your program is not infinitly recursive, in fact, there is no such thing.
Secondly, I could write a program to print the expression 'e^0' to the screen and thats never going to print a '1' digit. Does that mean e^0 is not equal to one? Actually '1' is not equal to the number that we think of as being one, it is just a character we use to represent it. 1 is an expression, just like 0.999... is an expression. What it LOOKS like is beside the point. It is the value of the number that is of interest to us. Not how it is written.

Last edited by mikau (2007-05-29 14:36:42)

Ricky · 2007-05-29 14:24:09

Nicely said Mikau.

mikau · 2007-05-29 15:54:52

Gracias! I've been trying to keep out of this thread but its starting to annoy me. Hehe!

Sekky · 2007-05-29 18:04:02

Anthony.R.Brown wrote:

So far no one on this site who thinks Infinite/Recurring 0.9 = 1 has ever shown the Math! or as you have asked about the Calculations!!...........

We've shown countless proofs, you choose to ignore every single one, because you're bigotted.

Anthony.R.Brown · 2007-05-30 02:17:21

To Sekky "ITS ABOUT TIME YOU SHOWED SOMETHING!"

A.R.B

Anthony.R.Brown · 2007-05-30 02:17:51

CAN WE TRUST COMPUTER PROGRAM RESULTS!?
----------------------------------------------------------

The answer to the Question above is yes! Providing we can see the source code and that we have an understanding of the language used.
But as programmers/manufacturers are not willing to do this because of possible counterfeiting their programs,and worst altering the actual programs! Then we just believe what the program tells us is true!
I have shown in my first Qbasic Infinite/Recurring 0.9 program above, just how easy it is to produce the results we want,without the program actually doing any Math calculations! If the source code was hidden most people would accept that it was calculating Infinite/Recurring 0.9
So if there is a Moral message in what I'm saying! Then it is don't believe the results 100% for programs like Mathematica6 etc. unless you have seen the source code etc.
Below is my second Qbasic Infinite/Recurring 0.9 program! This time it actually Calculates! The only Restriction is the Decimal Place Length! Other Languages produce longer Results...Understanding what is being Calculated is the most Important thing!.................................

REM ***************************************************************************
DIM START AS STRING
DIM A AS SINGLE
DIM B AS SINGLE
DIM C AS DOUBLE
DIM D AS DOUBLE
DIM RESULT AS STRING
CLS
PRINT
PRINT " INFINITE/RECURRING 0.9 QBASIC PROGRAM,By Anthony.R.Brown 30/05/07 "
PRINT
PRINT " YES! THIS PROGRAM ACTUALLY CALCULATES!........................... "
PRINT : PRINT
INPUT " PRESS < ENTER > TO RUN PROGRAM! "; START
CLS
PRINT : PRINT
REM *************************************************************************
CALCULATIONS:
A = 1
B = .9
C = A / B
D = C * B
IF D < 1 AND D <> 1 THEN RESULT = " Infinite/Recurring 0.9 < 1 and <> To 1 "
PRINT RESULT; D
PRINT : PRINT
PRINT " Length of Decimal Places Restricted By The Computer Language!.........."
END
REM ***************************************************************************

If you dont have a copy of the QBASIC program,it can be download for Free from

http://members.lycos.co.uk/brisray/qbasic/qind.htm

A.R.B

George,Y · 2007-05-30 02:44:03

Okay, mathematica6 do presume 0.999...=1. So the result from some software or a calculator cannot substantiate 0.999...=1. That's it. But can a software substantiate 0.999...<>1?

Softwares are made by humans, thus they only reflect the coders' respective recognition. So let sofware be software, debate be debate.

Anthony.R.Brown · 2007-05-30 02:51:19

Good point George,Y

But some programs have helped! like the "Four Colour Theorem Problem? " Example!

A.R.B

mikau · 2007-05-30 05:49:18

If the source code was hidden most people would accept that it was calculating Infinite/Recurring 0.9

No, most people wouldn't. Unless most people are morons.

Anthony, we are talking about an infinite number of 9's. Infinite! Your program is NOT infinitly recursive unless it prints an endless stream of 9's. ENDLESS as in, no last digit.

If you can write a program that can print as many 9's as Grayhams number, I'll be impressed but you will still not have provided enough 9's. You CANNOT print an infinite number of 9's in a finite amount of time, and even if you could, just because it doesn't LOOK like the digit 1 doesn't mean its value is not the same. cos(0) = 1, e^0 = 1, ln(e) = 1, and 0.9999... = 1.

You claim that no one has shown the math, or provided a proof that 0.999... is infact equal to 1, but you really are only denying the validity of the proofs we have already given because YOU say they are invalid!

You are actually the one that needs to show the math. You are the one that disagrees with an accepted and proven fact so its your job to disprove it. If you can't except the validity of the existing proofs, and question the fundamental principles upon which they are based, you might as well reject mathematics entirely and write your own book.

Anthony.R.Brown · 2007-05-31 01:08:54

To mikau

Quote:" Anthony, we are talking about an infinite number of 9's. Infinite! Your program is NOT infinitly recursive unless it prints an endless stream of 9's. ENDLESS as in, no last digit. "

A.R.B

It's not my program that stops" an endless stream of 9's. ENDLESS as in, no last digit." It's the Computer Language! Plus the Lack of Power from Any known Computer!.................................

Anthony.R.Brown · 2007-05-31 01:11:37

To mikau

Quote:" You claim that no one has shown the math, or provided a proof that 0.999... is infact equal to 1, but you really are only denying the validity of the proofs we have already given because YOU say they are invalid! "

A.R.B

All you have to do is show the Math from 0.999...(9) to 1 then you May have a Proof? so far AGAIN! no one has!..............................................................................................................

Maelwys · 2007-05-31 02:17:50

Anthony.R.Brown wrote:

All you have to do is show the Math from 0.999...(9) to 1 then you May have a Proof? so far AGAIN! no one has!

What do you mean by "show the math from 0.999... to 1"? There have been many proofs put forward on this thread showing that they both represent the same value. So there is no math from one to the other. If they have the same value, then by definition we don't need to add anything to get "from one to the other", which seems to be what you're looking for here, and what you're never going to get anymore than you could show me the "math from e^0 to 1".

mikau · 2007-05-31 08:32:04

It's not my program that stops" an endless stream of 9's. ENDLESS as in, no last digit." It's the Computer Language! Plus the Lack of Power from Any known Computer!.................................

mmhmm.. thats correct. Which is why your program is inconclusive. You do not posess the tools to run your 'infinite' program so what good is it?

All you have to do is show the Math from 0.999...(9) to 1 then you May have a Proof? so far AGAIN! no one has!

I have shown in my proof that 0.999... = 1 - 10^-∞

if this does not converge to 1 than the whole universe had bettter fly apart!

so what are you proposing 10^-∞ is equal to?

LQ · 2007-05-31 08:51:56

log(10^-inf) = -inf = -log(10^inf)

10^inf does not belong to S

neither does 1/10^-inf.

Last edited by LQ (2007-05-31 09:03:50)

Math Is Fun Forum

#676 2007-05-26 17:43:54

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

#677 2007-05-27 02:21:05

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

#678 2007-05-27 02:27:28

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

#679 2007-05-27 02:46:22

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

#680 2007-05-27 03:00:15

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

#681 2007-05-27 08:11:46

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

#682 2007-05-29 00:18:43

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

#683 2007-05-29 00:20:00

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

#684 2007-05-29 01:07:21

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

#685 2007-05-29 01:24:52

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

#686 2007-05-29 05:22:41

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

#687 2007-05-29 12:15:04

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

#688 2007-05-29 14:24:09

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

#689 2007-05-29 15:54:52

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

#690 2007-05-29 18:04:02

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

#691 2007-05-30 02:17:21

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

#692 2007-05-30 02:17:51

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

#693 2007-05-30 02:44:03

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

#694 2007-05-30 02:51:19

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

#695 2007-05-30 05:49:18

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

#696 2007-05-31 01:08:54

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

#697 2007-05-31 01:11:37

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

#698 2007-05-31 02:17:50

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

#699 2007-05-31 08:32:04

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

#700 2007-05-31 08:51:56

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

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