0.9999....(recurring) = 1?

Anthony.R.Brown · 2007-03-06 01:07:57

To Maelwys

Quot:
"I'm not sure I see your logic here... just because 1 < 9, 2 < 9, 3 < 9, 4 < 9, 5 < 9, 6 < 9, 7 < 9, 8 < 9, doesn't mean 9 < 9... you can't just create an arbitrary logic pattern and assume that it continues. Sorry, you need better logic than that. "

A.R.B

All you have to do!! is show a Number that Starts < 1 and <> 1 that is Recurring!

and is! or somehow becomes! > or = 1 and yet still conforms to the Definition Recurring!!

then you have won! the Argument! I'm Sure we will all have a long! long! Wait!......................

A.R.B

Maelwys · 2007-03-06 01:38:28

Anthony.R.Brown wrote:

All you have to do!! is show a Number that Starts < 1 and <> 1 that is Recurring!
and is! or somehow becomes! > or = 1 and yet still conforms to the Definition Recurring!!
then you have won! the Argument! I'm Sure we will all have a long! long! Wait!......................

What? Numbers can't "start <1 and somehow become >= 1". A number is a number, and doesn't change in any way. So of course I can't show you a number that magically changes. The problem seems to be your belief that 0.999... starts <1, which it doesn't. 0.999... = 1 at all times, it doesn't start <1 and become =1, it is simply = 1. And don't say "but it starts at 0.9" just because those happen to be the first couple digits of the number, because that doesn't mean anything at all. In mathematics, there is no such thing as a "single start value" that is equal to the first few digits of the number. A number is equal to what the number is, it is in no way equal to what the first few digits are (unless it's only those digits). I'm not sure how many more different ways I can try to make you understand that.

Anthony.R.Brown · 2007-03-06 01:56:32

To Maelwys

Quote:

" your belief that 0.999... starts <1, which it doesn't. "

in my Formula below B Starts as 0.9 and is < 1 everyone has agreed! it becomes Infinite 0.999...as C

---------------------------------------------------------------------------------------------------------------
INFINITE 0.9 <> 1 PROOF : FORMULA : By,Anthony.R.Brown,12/02/07
---------------------------------------------------------------------------------------------------------------

A = 1 " Single Start Value For 1 "

B = 0.9 " Single Start Value For 0.9 "

C ( A/B ) x B " Infinite 0.9 Value "

D ( A - C ) " Infinite < 1 Value "

C <> ( C + D ) " INFINITE 0.9 <> 1 "

Maelwys · 2007-03-06 02:05:23

Anthony.R.Brown wrote:

in my Formula below B Starts as 0.9 and is < 1 everyone has agreed! it becomes Infinite 0.999...as C

B doesn't "become" 0.999..., B is still 0.9, C is 0.999...
Using your logic I could just as well say "in your fomula, A starts equal to 1, and then by being divided by B and then multiplied by B, A becomes equal to 0.999..., proving that 0.999... = 1"

Dross · 2007-03-06 02:11:18

Anthony.R.Brown wrote:

All you have to do!! is show a Number that Starts < 1 and <> 1 that is Recurring!
and is! or somehow becomes! > or = 1 and yet still conforms to the Definition Recurring!!
then you have won! the Argument! I'm Sure we will all have a long! long! Wait!......................
A.R.B

Erm... how about 2.2222...?

Anthony.R.Brown · 2007-03-06 02:13:30

To Maelwys

Just for you ONLY! everyone else understands!!....................................................................

A = 1

B = 0.9 " Single Start Value For 0.9 "

B = ( A/B ) x B " Infinite 0.9 Value "

Anthony.R.Brown · 2007-03-06 02:15:58

To Dross!

Quote: " Erm... how about 2.2222...? "

A.R.B

2.2222...? Starts > 1 and <> 1

Maelwys · 2007-03-06 02:16:18

Anthony.R.Brown wrote:

A = 1
B = 0.9 " Single Start Value For 0.9 "
B = ( A/B ) x B " Infinite 0.9 Value "

That formula is clearly wrong though. Now you're trying to prove that 0.9 = 0.999...? In what world can B = A/B * B?

Anthony.R.Brown · 2007-03-06 02:25:15

To Maelwys

Quote:

"That formula is clearly wrong though. Now you're trying to prove that 0.9 = 0.999...? In what world can B = A/B * B?"

A.R.B

It's very clear! a Child could understand this Calculation!!

A = 1 " " A.R.B = " " A = 1 "
B = 0.9 " Single Start Value For 0.9 " " A.R.B = " " B = 0.9 "
B = ( A/B ) x B " Infinite 0.9 Value " " A.R.B = " " B = 1/0.9 x 1.111... "

As clear! as clear! can be!! Infinite 0.9 starts as 0.9 It then shows how it is/becomes Infinite!
I am afraid you have no argument! if you think you can just pluck a Value out of the sky! and call it an Infinite Number!

NOW YOU HAVE TO SHOW AS AN ARGUMENT! WHERE YOUR VERSION OF INFINITE 0.9 COMES FROM! AND I WANT TO SEE THE MATH!!

A.R.B

Maelwys · 2007-03-06 02:35:47

Anthony.R.Brown wrote:

It's very clear! a Child could understand this Calculation!!
A = 1 " " A.R.B = " " A = 1 "
B = 0.9 " Single Start Value For 0.9 " " A.R.B = " " B = 0.9 "
B = ( A/B ) x B " Infinite 0.9 Value " " A.R.B = " " B = 1/0.9 x 1.111... "
As clear! as clear! can be!! Infinite 0.9 starts as 0.9 It then shows how it is/becomes Infinite!
I am afraid you have no argument! if you think you can just pluck a Value out of the sky! and call it an Infinite Number!
NOW YOU HAVE TO SHOW AS AN ARGUMENT! WHERE YOUR VERSION OF INFINITE 0.9 COMES FROM! AND I WANT TO SEE THE MATH!!

I'm not arguing against the idea that 1/0.9 * 0.9 = 0.999..., I completely agree with that. However, I also argue that X/Y * Y = X for any X, and any Y <> 0; which means that 1/0.9 * 0.9 = 1 as well, meaning that 0.999... = 1. I also take issue that B = A/B * B, because you can't change the value of a variable halfway through an equation, which makes it appear that you're saying 0.9 = 0.999..., which is definitely not the case. If you want to go back to saying C = A/B * B, I'm okay with that, but I'll continue to use my proof above to show that C = A, and D = 0.

Last edited by Maelwys (2007-03-06 02:37:09)

Anthony.R.Brown · 2007-03-06 02:45:19

To Maelwys

A.R.B

Better than that!! Answer my Main Question for once!

" NOW YOU HAVE TO SHOW AS AN ARGUMENT! WHERE YOUR VERSION OF INFINITE 0.9 COMES FROM! AND I WANT TO SEE THE MATH!! "

George,Y · 2007-03-06 02:52:50

Ok, let's say what guarantee the 0.999... having all finite digits, or finite 9's:

First, it sounds convenient to say that 9's in 0.999... carry on and on. But this only mean counting one digit, two digits, three digits, ... without a stop. This is equivalent to saying 0.999... means the series {0.9, 0.99, 0.999, 0.9999,...}. You can indeed get any finite 9 from some of its elements or after some steps, but this form of 0.999... is far from ideal. It is a Growing series, indicating the process of growth is not over and much worse, the process of growth is still in the finite stage. Yep, in finite stage, a stage cannot meet your demand to equate 0.999... to 1 unless you "aquire" it by deceptive definition.(you "define" it)

Let's say there is yet another alternative for 0.999.... How about it having got infinite 9's already and still endless? 0.999..., this time, is indeed able to accommodate any finiteth 9 and meet the property that 0.999... has no difference than 1 and meet your conception that it's without a stop without a last 9. And this form means 0.99...999...-you have got an infinite amount of 9's at hand and the 9's are still endless.

What? you wanna argue that it shall be 0.999... endless instead? This statement makes no sense- without mentioning the word "infinite" you admit 0.999... is the first structure, which avoids getting infinite 9's already but is blocked in the endless stage having only finite 9's . Unless, you say that one step of it or one element of it has already got infinite 9's. But this saying gets back to the second structure again.

So, let's go back to the second structure of 0.999.... Now that you have got infinite amount of 9's and the 9's are still relentlessly endless. In this way you ban me from investigating the last 9.(I only investgated the infiniteth 9 actually) And you have other orders banning from me to express the infiniteth 9, like the infiniteth is invalid in maths terminology, like the 9 after infinite-1 9's only mean the 9 after infinite 9's. ...Wait, I have got the inspiration:

I give up finding the infiniteth 9, but I am sure that I can get the 9 Just After Infinite 9's in the second structure. This is the natuaral derivative from the property of infinite 9's already and still endless. So what does this 9 Mean then? What does the 9 before this 9 Mean then? What does the 9 before the previously mentioned 9 Mean? Come on! Guess!

0? 9×10^∞? real infinitesimal? quantitiless? You know the consequence of these answers, don't you? If you don't, go back to Post 96 or Post 107.

Well, you may question that can I count to the 9 after the infinite 9's? But this question only means that your mind is unclear enough to go back to the first form or you only want to defend your position by double standards-you accept the convenience of the second form and throw the delima of the first form on me at the same time. Let's settle this problem by Dross's honest remark-
" Can't you imagine having infinite 9's altogether? It's your inability to count them over." (isn't word by word by Dross, but the meaning is his)

Now, let's say there is another structure of 0.999..., infinite amount of 9's but not endless, this doesn't satisfy you either, am I right? If you know another structure that enables 0.999... to have "any" "all" finiteth digit in it, please specify.

______________________________________________________________________________
Next, my answer to your integer problem. Take it easy. Let's have a quiz!
A pile of apples has this property: you can get any positive integer amount of apples out of it, or in other words, you can count to any positive integerth (i.e. 2nd, 1millionth) apple in it. The question is, listen carefully, how many apples does the pile have?
Infinite!

Next question: please substitute apples by 9's and substitute apple by 9 and substitute pile by bunch in the previous question and make up a new question. Who volunteers this time? Hands up!

George,Y · 2007-03-06 02:54:07

Telling so much about 9's or ... is really exhausting, break time. Allow me to tell a story.

2000 years ago in my country, the iron was very precious. And it was common to hang iron bell in rich towns for telling time. One poor man in one of these towns had an dream, he dreamed he could get rich by stealing the bell and sell it. But the bell was huge and heavy, a tiny drop while moving it could make a loud an lasting sound. The man thought and thought, finally he came up with an idea. The sound takes effect only when it is heard. So he filled his ear with cotton, dense cotton. He went to steal the bell at night. Not surprisingly, he made an error and the heavy bell hit the ground, woooo...n! Suddenly he was surrounded by the crowd and was arrested.

By avoiding hearing the sound doesn't stop it from existing. By avoiding mentioning the infinity can stop it from existing?

Well, there might be another solution. Right, fill cotton into everyone's ears in the town! Or contaminate the water with a special drug to let them sleep. This method is also written in another story, this time, by a Danish.

The story was "The emperor's new suit ", written by the famous children story writer Hans Christian Anderson. Many of you might be familiar with this story. But it is wise to tell the basic line of it in case someone might haven't heard of it.

Three liers wanted to get money from a king. They claimed they could knit a fine and magic suit that only intelligent people can see. In other words, the suit is only visible to intelligent people. They demanded gold threads, diamonds for making the suit, and they grab them to their own pocket not suprisingly.

Many officials and nobles had been sent to see what was going on about the suit making. And all of them reported how beautiful the suit was vividly. The tailors only showed them nothing but described the "cloth", the "unfinished suit" vividly, adding one sentence at last,"My dear and intelligent majesty, can't you see how beautiful it is?"

Finally the three left before the deadline and left a note stating the "suit" was just hanged there. The "intelligent" king "put up" this "holy suit" without any "ordinary clothes". Put it another way, he was naked.

The king held a parade. People gather, and yelled "How beautiful!" "Fantastic!" "Wonderful!" But one five-year old boy asked his parents"Why is he so happy wearing nothing?!"

Okay, time to think. How did the three liers block almost all people's mouth? He didn't use cotton or drug. He only sharp shot any people objecting him by indicating they were not intelligent.( You are intelligent, then follow my description.) Clever.

So why are so many rules about infinite digits, infinity all around? Like having got infinite digits but banning stating the infiniteth digit? Like having all the finiteth digit but banning the existence of infinite amount of digits already? "We" have the rules, "we" know orthodoxy maths, so obey us.

There haven't been more rules and so many bans than in the area of infinity, infinite digits. I am sick and tired of these rules designed to ban discussion. And I have refuted them in my previous post. All my necessary refutations are done. If anyone keeps talking to me "you cannot say this, you cannot say that" in any post after this one, please read carefully all my posts on this subject. If you don't get it, I personally interpret you keep the bias that you shall win and that 0.999... shall equal to 1 much more probably than you really don't understand. Thus I will not write back and this post is highly probably my last one on this subject.

Study well, Live happily, everyone! Bye in this thread!

Maelwys · 2007-03-06 03:06:06

Anthony.R.Brown wrote:

To Maelwys
A.R.B
Better than that!! Answer my Main Question for once!
" NOW YOU HAVE TO SHOW AS AN ARGUMENT! WHERE YOUR VERSION OF INFINITE 0.9 COMES FROM! AND I WANT TO SEE THE MATH!! "

Umm... read the first line of my reply above. "I'm not arguing against the idea that 1/0.9 * 0.9 = 0.999..., I completely agree with that. "
So I agree with you that A/B * B = 0.999..., I just also happen to believe that A/B * B = A = 1, which means that 0.999... = 1

Anthony.R.Brown · 2007-03-06 03:18:07

To Maelwys

Quot: " Umm... read the first line of my reply above "

A.R.B

You obviously cant think for yourself! don't copy my examples! put something forward yourself! or are you afraid of it being ripped to pieces! by me showing you any Infinite Number Starts from a Single Value!

Maelwys · 2007-03-06 03:31:24

Anthony.R.Brown wrote:

To Maelwys
Quot: " Umm... read the first line of my reply above "
A.R.B
You obviously cant think for yourself! don't copy my examples! put something forward yourself! or are you afraid of it being ripped to pieces! by me showing you any Infinite Number Starts from a Single Value!

I answered your question, with a formula that we can both agree on, to ensure that we have a common point of understanding, and now you're insulting me for it? You asked me "NOW YOU HAVE TO SHOW AS AN ARGUMENT! WHERE YOUR VERSION OF INFINITE 0.9 COMES FROM! AND I WANT TO SEE THE MATH!!" and I answered "1/0.9 * 0.9 = 0.999..." which is all the math you need, and it's something that I already know you agree to (so once less thing for us to argue about) and you're refusing it as an explanation simply because you stated it first?

Alright, here's a different one. 1/3 * 3 = 0.999... 1/3 = 0.333... * 3 = 0.999... Agreed?

Last edited by Maelwys (2007-03-06 03:36:38)

luca-deltodesco · 2007-03-06 03:36:59

oh ok then.

LETS MAKE THIS CLEAR!!! ONCE AND FOR ALLL!!! FOR ALL YOU IDIOTS THAT DONT UNDERSTAND!!! IM GOING TO CREATE NEW VARIABLES, BECAUSE DOING THIS MAKES THINGS EASIER TO UNDERSTAND

X = 1
Y = 0.9

Z = 1/0.9 = 1.111111111111. INFINITE 1.1
Z * 0.9 = 0.9999........... INFINITE 0.9

Z * 0.9 = 1/0.9*0.9 = 1..... oh math.

I WILL NOW SHOW THAT X/Y*Y DOESNT EQUAL X BY USING A CALCULATOR.... (finds windows calculator... AHAH!)

AHAHA NOW ALL YOU FOOLS WILL SEE!!! HOW STUPID YOU ALL ARE!!!

(goes to windows calculator, types in 1/2, gets 0.5, types in *2, gets 1... oh math, not again!!! stupid calculator giving me the wrong result!!!! LOLOLOLOl types in 1/0.9, gets 1.111...., types in *0.9, gets 1... LOLOLWTF WINDOWS CALCULATOR IS BROKEN LOLOLOL)

AHAHA I HAVE NOW PROVEN THAT INFINITE 0.9 <> 1 ALL YOU IDIOTS ARE WRONG!!!

... crys in corner

oh and yes, windows calculator actually does give that result, although a less precise one would not.

Maelwys · 2007-03-06 03:54:38

luca-deltodesco wrote:

oh and yes, windows calculator actually does give that result, although a less precise one would not.

Lol, that's funny... all this time debating and I never even thought to try punching that formula into windows calculator. I just assumed that it rounded to 32 digits (although that's impressive in itself) and would give the 0.999... result for the formula. Apparantly it's smarter than I gave it credit for, with regards to infinitely repeating decimals. ;-)

Anthony.R.Brown · 2007-03-06 04:22:46

To Maelwys

Quote:

" Alright, here's a different one. 1/3 * 3 = 0.999... 1/3 = 0.333... * 3 = 0.999... Agreed? "

A.R.B

Firstly using fractions is not accurate! you cant get a true 1/3 Decimal Value!

i.e give me 3 Single Decimal Values of equal Value! that equal 1

Allowing for your mistake! you are now agreeing with me! that your version of Infinite 0.9 has come from the single Value of 0.333... x 3

But just as I said! from the first Decimal point onwards when there is a total Value of 0.9 this is the first single value for your version of Infinite 0.9

Maelwys · 2007-03-06 04:27:48

Anthony.R.Brown wrote:

" Alright, here's a different one. 1/3 * 3 = 0.999... 1/3 = 0.333... * 3 = 0.999... Agreed? "
A.R.B
Firstly using fractions is not accurate! you cant get a true 1/3 Decimal Value!
i.e give me 3 Single Decimal Values of equal Value! that equal 1

I wasn't using fractions, I was expressing a division of 1 divided by 3 * 3 (the same way you were dividing 1/0.9 * 0.9). Yes, my 1 divided by 3 = 0.333... is a repeating value, the same way that your 1 divided by 0.9 = 1.111... is a repeating value.

Anthony.R.Brown wrote:

Allowing for your mistake! you are now agreeing with me! that your version of Infinite 0.9 has come from the single Value of 0.333... x 3
But just as I said! from the first Decimal point onwards when there is a total Value of 0.9 this is the first single value for your version of Infinite 0.9

There you go on about the "single value" again, which I still don't understand or recognize as any valid math theory. I really have no idea what this last sentence of yours means (or should I say sentences, since there seems to be punctuation randomly in the middle of it).

Ricky · 2007-03-06 04:29:24

There haven't been more rules and so many bans than in the area of infinity, infinite digits. I am sick and tired of these rules designed to ban discussion. And I have refuted them in my previous post. All my necessary refutations are done. If anyone keeps talking to me "you cannot say this, you cannot say that" in any post after this one, please read carefully all my posts on this subject. If you don't get it, I personally interpret you keep the bias that you shall win and that 0.999... shall equal to 1 much more probably than you really don't understand. Thus I will not write back and this post is highly probably my last one on this subject.

There is a very simple reason why there are such "bans". Because infinity has been banned from being included with the real numbers. Every single time I have "banned" you from saying something, I have given a reason for it. For example, you are "banned" from talking about the infiniteth digit because the digits in a decimal expansion are countable, and thus all a finite distance away from the decimal point. You are "banned" from talking about the infiniteth digit because it doesn't freakin' exist. Just like I am banned from talking about the well defined inverse of a non 1-1 function because it doesn't exist. Just like I am banned from talking about f:R->R at f(infinity) because infinity isn't in the domain.

It doesn't exist, so why talk about it.

Sheesh.

Anthony.R.Brown · 2007-03-06 04:44:27

To Maelwys

Quote:

" There you go on about the "single value" again, which I still don't understand or recognize as any valid math theory. I really have no idea what this last sentence of yours means (or should I say sentences, since there seems to be punctuation randomly in the middle of it). "

A.R.B

The most important thing to do with any Argument! is knowing where the Numbers have come from! and how they are made!

Maelwys · 2007-03-06 04:51:53

Anthony.R.Brown wrote:

To Maelwys
Quote:
" There you go on about the "single value" again, which I still don't understand or recognize as any valid math theory. I really have no idea what this last sentence of yours means (or should I say sentences, since there seems to be punctuation randomly in the middle of it). "
A.R.B
The most important thing to do with any Argument! is knowing where the Numbers have come from! and how they are made!

A number is a number, and the value that is has is the value that it has. 0.999... has a value of 0.999..., it doesn't have a value of 0.9 anymore than it has a value of 42, and it never did.

Anthony.R.Brown wrote:

Because we are Calculating an Infinite Number!! and Calculators Round the Number up!!
Lets look at the Start again!
Infinite 0.9 "one Decimal place " x 1.1 = 0.99
Infinite 0.9" two Decimal place's " x 1.11 = 0.999

Those aren't infinite numbers, those are real numbers (you're just multiplying 0.9 x 1.1, no infinite-long recursions involved in that). You can't apply normal rules for finite numbers into infinitely recursive numbers, just like you can't apply normal rules for finite numbers into infinity. Infinity + 1 = Infinity, but if you said that about any real number, you'd be wrong (1 + 1 = 1 is an incorrect statement, for example).
0.9 x 1.1 <> 1
0.9 x 1.11 <> 1
but
0.9 x 1.111... = 1

Lets take this a different way. For any two different numbers, M and N, there is always a 3rd number P that can be added to M to equal N, because P expresses the difference between the two numbers. There is also always a 4th number Q that can be multiplied by M to equal N, because Q expresses the ratio between the numbers.
So, if
M = 0.9
N = 1
What do you believe the numbers P and Q are?

Anthony.R.Brown · 2007-03-06 04:52:08

To mathsyperson

This is the Sister thread! the other one got no response! lets keep it fare!

A.R.B

Maelwys · 2007-03-06 04:55:46

Anthony.R.Brown wrote:

To mathsyperson
This is the Sister thread! the other one got no response! lets keep it fare!
A.R.B

By "sister thread" I think he meant that he'd also close the "proof why 0.999... = 1" thread that you created your thread in retaliation to. Now both are closed, and all of the discussion about this should continue on this thread alone.

Math Is Fun Forum

#501 2007-03-06 01:07:57

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

#502 2007-03-06 01:38:28

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

#503 2007-03-06 01:56:32

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#504 2007-03-06 02:05:23

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#505 2007-03-06 02:11:18

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#506 2007-03-06 02:13:30

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#507 2007-03-06 02:15:58

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#508 2007-03-06 02:16:18

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#509 2007-03-06 02:25:15

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#510 2007-03-06 02:35:47

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#511 2007-03-06 02:45:19

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#512 2007-03-06 02:52:50

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#513 2007-03-06 02:54:07

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#514 2007-03-06 03:06:06

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#515 2007-03-06 03:18:07

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#516 2007-03-06 03:31:24

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#517 2007-03-06 03:36:59

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#518 2007-03-06 03:54:38

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#519 2007-03-06 04:22:46

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#520 2007-03-06 04:27:48

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

#521 2007-03-06 04:29:24

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#522 2007-03-06 04:44:27

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

#523 2007-03-06 04:51:53

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

#524 2007-03-06 04:52:08

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

#525 2007-03-06 04:55:46

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

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