0.9999....(recurring) = 1?

Anthony.R.Brown · 2007-02-02 01:00:41

( 0.9r "Definition" ) <> 1 ) "Now that,s Beautiful!"

Can others please put forward their Definition of "Recurring"

A.R.B

kylekatarn · 2007-02-02 01:59:44

Dross wrote:

Ah, the irony! I opened up Wikipedia to find that the subject of this thread is also the topic of their article of the day
Have a gander at the main page, or the article itself if you're not reading this today.
And yes, I know - "just because it's on the internet doesn't make it true". But seriously, if you disagree with 0.999... = 1, have a look at the article. A REAL look and really READ it - it may just clarify something you didn't even think was important, or didn't think to think about at all. Or it may just be explained in a way that you "get".

People need to have a deeper understanding of series before accepting that 0.9... == 1

It happened with me ;p

George,Y · 2007-02-03 15:01:42

I suggest you to read #59 to #63, and #107

Anthony.R.Brown · 2007-02-06 00:51:39

To George,Y

Quote: " I suggest you to read #59 to #63, and #107 "

Very Good George!!

A.R.B

kylekatarn · 2007-02-06 04:00:46

The day you have lectures on Limits and Infinite Series, come here again and you will make a little smile when re-reading your theories

George,Y · 2007-02-06 16:43:13

kylekatarn wrote:

The day you have lectures on Limits and Infinite Series, come here again and you will make a little smile when re-reading your theories

Are you suggesting that Ricky doesn't know limits and infinite series? (Around post 60 he admitted "we simply defined it in limits")

Ricky · 2007-02-06 16:47:04

No George. He was talking to ARB. I think you're getting threads mixed up.

George,Y · 2007-02-06 16:52:58

Uh, then it is really perplexing...

Toast · 2007-02-06 19:38:15

I really don't understand the notation of

(0.9r "Definition") <> 1)

What is <>, what is r, and "Definition"...

kylekatarn · 2007-02-07 00:02:08

George,Y wrote:

kylekatarn wrote:
The day you have lectures on Limits and Infinite Series, come here again and you will make a little smile when re-reading your theories
Are you suggesting that Ricky doesn't know limits and infinite series? (Around post 60 he admitted "we simply defined it in limits")

It wasn't a suggestion. Someone who doesn't ""believe"" 0.(9) = 1 it's because one of two things:
- he/she doesn't really know that 0.(9) is formed by the infinite sum 0.9 + 0.09 + 0.009 + ... = 1
- he/she may know limits and infinite series but he/she is trying to show something completely out of Mathematics. 0.(9) equals 1, whether one likes it or not.

All it took me to understand and accept the equality of 0.(9) and 1 was notion of limit and infinite sum. Understand, not just "knowing about". If someone really understands but keep saying "0.(9) ≠ 1 because of this", "0.(9) ≠ 1 because of that", "0.(9) ≠ 1 because of the infinite difference Z ou W" then something is wrong.

Last edited by kylekatarn (2007-02-07 00:07:07)

George,Y · 2007-02-07 00:58:04

kylekatarn wrote:

Someone who doesn't ""believe"" 0.(9) = 1 it's because one of two things:
- he/she doesn't really know that 0.(9) is formed by the infinite sum 0.9 + 0.09 + 0.009 + ... = 1
- he/she may know limits and infinite series but he/she is trying to show something completely out of Mathematics. 0.(9) equals 1, whether one likes it or not.
All it took me to understand and accept the equality of 0.(9) and 1 was notion of limit and infinite sum. Understand, not just "knowing about". If someone really understands but keep saying "0.(9) ≠ 1 because of this", "0.(9) ≠ 1 because of that", "0.(9) ≠ 1 because of the infinite difference Z ou W" then something is wrong.

Then could you mathematically explain how does 9's 0.999... represent from finite rationals to infinitesimals? I SUGGEST you to reread Post 107 and around and then answer this question by whatever you know or think.

George,Y · 2007-02-07 01:00:44

Or Post 96, on the 4th page

George,Y · 2007-02-07 01:02:10

<>means≠

kylekatarn · 2007-02-07 02:06:19

Dross wrote:

when you write down 0.999..., you may be asked to define what you really mean by that. Note that:
So, what we really mean when we write down 0.999... is:
Which, if we were to be fully rigorous, means that:
So the above is what we really mean by 0.999... - so the question is, is the above expression equal to one? Well... yes, it is.

There isn't much more to say on this subject, the proof is there, the symbols, notations, the meanings. If you, Anthony and others don't accept 0.(9) = 1, that's fine to me. You are free to reinvent algebra and calculus if you want to, but I prefer to stick with concepts that have been developed through centuries of mathematical research.

Last edited by kylekatarn (2007-02-07 02:14:52)

Anthony.R.Brown · 2007-02-07 03:00:37

To kylekatarn

From another post of mine! can you give a Value for N4 = " Maximum possible Infinite 0.9's "

Because I can always give ( N4 ) + another .9

luca-deltodesco · 2007-02-07 03:26:35

if there are an infinte amount of 9's, then adding another 9 changes nothing

George,Y · 2007-02-07 14:48:23

luca-deltodesco wrote:

if there are an infinte amount of 9's, then adding another 9 changes nothing

Exactly, that is within defination. But the dilema is substracting another 9, another 9, and another 9 changes nothing as well.

∞-n=∞

The more interesting thing is, even if you substract a proportion of infinity of 9's, you still change nothing.

∞-p∞=∞, 0<p<1

So, is there an answer to the question that from where the 9's become valueless?
0.9999...999...

I bet nobody can figure it out because the concept of infinity itself is an awkward imagination.

Anthony.R.Brown · 2007-02-08 00:41:22

To George,Y

Wonder full Stuff! Now I think the Penny is Starting to Drop! with the Non - Believers!

I think we will have to set up a post for the!

" Past Proved Wrong! Math is Fun Forum Members! "

A.R.B

Dross · 2007-02-08 02:03:59

Anthony.R.Brown wrote:

I think we will have to set up a post for the!
" Past Proved Wrong! Math is Fun Forum Members! "

MathsIsFun, can we change ARB's title from "Full Member" to something like: "I Am Wrong". Seriously - he may try and give advice in the Help Me! section on other things he doesn't know diddly-squat about, and some poor student could read his response before we get there to cull the stupidity.

mathsyperson · 2007-02-08 03:17:29

That's a bit mean. Just because Anthony won't accept that 0.(9) = 1 (and most people refuse to believe its truth when they first see it) doesn't suddenly imply that any statement he ever makes will be false.

Besides, it looks like he's only here to convince people of his view on this subject, and not to post anywhere else.

Ricky · 2007-02-08 09:48:07

Agreed mathsyperson. Judging intelligence based on ones knowledge of a single subject, nay, a single problem, seems to be rather, well, stupid.

Dross · 2007-02-08 11:27:51

C'mon, we all know that Mr. Brown's reluctance to accept that 0.9999... = 1 isn't the only thing he's said that reveals something about him. The things which he says, more specifically the way he will ignore points of view that seem correct purely because they contradict him and his views, the way he will ignore questions that are both important and irrelevant for the same reasons...

I place a lot of value on being able to reason. The validity of an argument, whether it is sound... it's all very important to me. This guy would take the essay I wrote on argument structure and use it as a handkercheif - not because he wanted to be rude to me personally, but because he thinks it doesn't matter. If Frege himself were to sit ARB down and have a chat with him about logic, Anthony would probably snub every other claim he made. Gottlob could back himself up - ARB would shpout non-sensical drivel until one of them got tired and went home.

The denial of 0.9999... = 1 isn't what makes me class Anthony as not being inteligent - but the way he does so in a very unstructured, very unstable way does.

Hell, it's even been seen that what he says is self-inconsistent, something which I utterly detest and cannot help but think absurd!

I used to think he was taking the mickey (surely nobody can contradict themselves like that and mean it! (well, according to many they really can't!) ), but now I'm not so sure...

Anthony.R.Brown · 2007-02-09 00:53:51

To Dross!

Do Something Constructive and answer the Question Below!

Instead of trying to make your own self centred opinion about everything!
I waste so much time Paging past the Rubbish you Post on this Forum!
All we want from you is Answers Only! to do with Math! Keep your opinions to your self!!

From another post of mine! can you give a Value for N4 = " Maximum possible Infinite 0.9's "

Because I can always give ( N4 ) + another

Dross · 2007-02-09 02:36:54

Anthony.R.Brown wrote:

From another post of mine! can you give a Value for N4 = " Maximum possible Infinite 0.9's "
Because I can always give ( N4 ) + another

This question has already been answered (by Luca, if I recall correctly) but "what the hey", I might as well essentially repeat what he said.

Anyway - I see what you're getting at. If I were to give you:
0.9999999999999999999999, you'd say "well hang on a minute, we can have:
0.99999999999999999999999" - right?

Well, if we have an infinite number of nines after the decimal place, you cannot do this, since the 9's never end.

So the answer to your question is an infinite number of 9's after the decimal place.

Anthony.R.Brown · 2007-02-10 01:33:22

Quotes:

"Well, if we have an infinite number of nines after the decimal place, you cannot do this, since the 9's never end."

"So the answer to your question is an infinite number of 9's after the decimal place."

So now we all agree! there is no End to the .9's

Math Is Fun Forum

#326 2007-02-02 01:00:41

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

#327 2007-02-02 01:59:44

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#328 2007-02-03 15:01:42

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#329 2007-02-06 00:51:39

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#330 2007-02-06 04:00:46

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#331 2007-02-06 16:43:13

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#332 2007-02-06 16:47:04

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#333 2007-02-06 16:52:58

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#334 2007-02-06 19:38:15

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#335 2007-02-07 00:02:08

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#336 2007-02-07 00:58:04

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#337 2007-02-07 01:00:44

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#338 2007-02-07 01:02:10

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#339 2007-02-07 02:06:19

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#340 2007-02-07 03:00:37

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#341 2007-02-07 03:26:35

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#342 2007-02-07 14:48:23

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#343 2007-02-08 00:41:22

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#344 2007-02-08 02:03:59

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#345 2007-02-08 03:17:29

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#346 2007-02-08 09:48:07

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#347 2007-02-08 11:27:51

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#348 2007-02-09 00:53:51

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#349 2007-02-09 02:36:54

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#350 2007-02-10 01:33:22

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