Simple mathematical problem (?)

[xouper]

clk:

S = 1 + 2 + 4 + 8 + 16 + 32 + 64 +...
so
2S = 2 + 4 + 8 + 16 + 32 + 64 +...
so
2S = S-1
solve for S to get:
S = -1
so...
1 + 2 + 4 + 8 + 16 + 32 + 64 +... = -1 !
How do you like them apples?

Since it looks like we have an interesting change of topic here, I created a new thread for it and posted my reply to you there.

http://www.randi.org/vbulletin/showthread.php?s=&threadid=30154

I am hoping we can continue the p-adic conversation there instead of here, and leave here for the original topic about 0.999... = 1.

 

[davefoc]

1 - .999.... = an infinitely small number

infinitely small number = 0

1 - .999... = 0

1= .999...

Is an infinitely small number = 0 ?

My thought is yes. It would be improper to say that it approaches 0 as it is infinitely close to zero and is therefore as close to zero as it is going to get.

The series .9 + .09 + .009 + ... approaches 1. As you add terms it gets closer and closer to 1. If the series has an infinite number of terms it doesn't approach one, it is one.

I realize that I'm saying what others have said, my apologies for not crediting them. I am just restating in my own words.

 

[Kumar]

There can be some other maths problems. Just tell me how it can be:-

7 X 9 = 79

7 + 7 = 27

??????????????

 

[BillyJoe]

There can be some other maths problems. Just tell me how it can be:-

7 X 9 = 79

7 + 7 = 27

A X B = AB
A + A = 2A

BillyJoe.
(YOU IDIOT!)

 

[mummymonkey]

I'm no mathmatician having slept through maths at school. I also skimmed a lot of this thread so please forgive me if this is a repeat. My understanding is this:

1/3 = .3 rec
Multiply both by 3 to get
3/3 = .9 rec
3/3 is equal to 1
Therefore
1 = .9 rec

The only way this can be wrong is if you think the first line is incorrect. That being so, the argument is one of semantics only. It may not be the case that 1 equals .9 rec in the same way that 4 apples does not equal 4 oranges, but they do represent the same number. How did I do?

 

[Kumar]

Hello Billy Joe,

Originally posted by KumarThere can be some other maths problems. Just tell me how it can be:-

7 X 9 = 79

7 + 7 = 27
--------------------------------------------------------------------------------

A X B = AB
A + A = 2A

BillyJoe.

Thanks most inteligent indication. You are good in maths. 100/100 marks . You was unnecessary discussing other subjects.

 

[Earthborn]

How did I do?

I think you actually proved that learning while you sleep actually works!

And it works even better than completely misunderstanding surreal number theories by brilliant mathematicians.

 

[TillEulenspiegel]

bjornart: You're both missing that ...999 is actually the same as infinity.
...999 = ...888 = ...777 and so on.

Ok I'm dense, plot on a 4 quadrent, graph the trend of different sets of an infinite series of repeting mumbers and show the intersection. ( use the quoted series) ...999,...888,...777

Being a LUX adherent and because this thread should have died a natural death ...BUT NO! =)
J/k J/K

 

[BillyJoe]

Hello Billy Joe,

Thanks most inteligent indication. You are good in maths. 100/100 marks . You was unnecessary discussing other subjects.

Yes, sometimes I just mess about but it is never with evil intent. My new signature is directed at you but, of course, is a joke. I tried a serious discussion with you before but got lost in misunderstanding which I attribute to your poor command of English which, of course, is not your fault.

I am happy we have had at least one clear exchange.

BillyJoe.
(BTW, I am an IDIOT as far as maths is concerned. I had to be dragged to the conclusion that 0.9~ = 1 (not in this thread but another a couple of months ago). But it didn't take me as long as LuxFerum though )

 

[angard]

Hey,

I just realized what iota is.

Just find out who is the last poster in this infintie(if it was) long thread.

j/k

\\Mike

ps. I like when people agree.

 

[Igopogo]

Hi all, I'm new here i late to this thread, so sorry for dragging it up to the top.

Before reading this thread, if you asked me to name the closest number to 1, without being equal to it, I would have said .9999….& I still would after reading it.

I’m no mathematician, but one proof here I can understand & question is:

"1/3 = .3 rec
Multiply both by 3 to get
3/3 = .9 rec
3/3 is equal to 1
Therefore
1 = .9 rec"

I think this assumption is flawed:

3(.333…)=.999...

since you have to be able to start multiplying from the low end of the number in case you have to round up.

For example, we know:
3(.33333)= .99999 and
3(.33334)= 1.00002, so
3(.333…)= ?

Since no matter where you start multiplying, from there are still an infinite number of 3’s left to go to the right, so the answer .999… is an assumption not taking into account the whole number.
I would suggest that 3(.33333…)=1.000, not .999…

My proof is:
1/3=.333…
so therefore 3(.333…)=1

Also, we know from dividing 1/3, that no matter where you stop, there's a remainder left that is a 1 in the last digit position. Taken into account when multiplying, I think it's safe to assume that if you "could" multiply out the infinity of 3's, it would be equivalent to the remainder, thus rounding the .9999... up to 1.0000

 

[xouper]

Igopogo: I’m no mathematician, ...

And yet you feel qualified to tell mathematicians they are wrong? Fascinating.

By the way, welcome to the forum.

 

[Zep]

Interesting conversation with a PhD in Mathematics the other day... Showed him this problem and the proofs provided by people above.

His initial comment: This has always been a grey area and subject of much argument. While the calculation of the limit value is indeed correct, one first needs to understand what is meant by performing the limit calculation, why it is done in the first place. So intuitively it would seem that there is not an equality in real terms, although there is very nearly one! But infinity is a funny thing so I'll get back to you when I've thought about it some more!

So... Umm. I'll wait and ask again soon! Meanwhile, I'm still plunking for an inequality of the series itself, whereas I'm more than happy that the limit of same is indeed unity (as accepted by me originally).

 

[Igopogo]

Thanks for the welcome Xouper. I'm not here to tell mathematicians they're wrong as I didn't realize they were all on one side of the arguement. Anyways, the post I quoted started with the words "I'm no mathmatician" as well, so I felt qualified enough to answer that one.

 

[davefoc]

Igopogo,
Welcome to the forum. This is a strange thread and it was surprising to find that somebody's first post would be to this thread.

I think the issue is not quite as straightforward as it seems with regards to the subject of this thread.

Although there have been several esoteric proofs put forward (and some that weren't quite valid IMHO like the one you referenced) I think the issue is more convincingly dealt with by discussion than with proofs.

The argument that .999... equals one and doesn't approach one is based on the idea that there is an infinite number of 9's represented in that notation. That doesn't mean that you can add another nine and get closer to one than before you added that nine. That means that there are already an infinite number of nines there. You can't just add another nine to the nines already there, it's already been added.

Besides the above thinking, I also found Earthborn's argument persuasive in the early part of this thread that there is not a non-zero number that exists between .999... and 1. In other words 1 - .999... = 0. Or simply put .999... = 1.

If you don't find any of the above persuasive, then perhaps you might consider that Xouper says that .999... = 1 and I have no reason to believe that Xouper is ever wrong.

 

[xouper]

Zep: Interesting conversation with a PhD in Mathematics the other day... Showed him this problem and the proofs provided by people above. His initial comment: This has always been a grey area and subject of much argument.

I beg your forgiveness for not knowing how to say this in a compassionate manner, but I am skeptical that you reported his comments correctly. I am not aware of any gray area or argument about this among mathematicians. There has, however, been much grayness and argument from students and non-mathematicians who do not yet sufficiently understand the concepts.

Did you ask that PhD person whether there exists positive integers A and B such that A does not equal B, and A / B = 0.999...? I would like to know what his answer to that is, and whether there is any gray area or argument about it in the math community.

Igopogo: I'm not here to tell mathematicians they're wrong as I didn't realize they were all on one side of the arguement.

To clarify, yes they are all on one side of the argument.

daveofc: If you don't find any of the above persuasive, then perhaps you might consider that Xouper says that .999... = 1 and I have no reason to believe that Xouper is ever wrong.

That gave me a chuckle.

It's always appropriate to question if I am wrong. In this particular case, you don't even need to take my word for it. My advice to anyone is go ask a professional mathematician or a professor of mathematics at the local university or college. Ask them two questions:

• Is 0.999... = 1?
  
• Is there any gray area or disagreement in the math community about the answer?

 

[xouper]

Zep: So intuitively it would seem that there is not an equality in real terms, although there is very nearly one! But infinity is a funny thing so I'll get back to you when I've thought about it some more!

May I make a suggestion? As long as you try to analyze the problem from Zeno's perspective, it will always be a paradox. I'd suggest abandoning that approach. I don't yet know which approach will ding the bell for you, but may I suggest looking at the rule for converting the decimal expansion of rational numbers to their fractional equivalent.

 

[Zep]

Nope, that's what he said, in so many words. Certainly I am not quoting him absolutely verbatim. Perhaps I paraphrased it poorly but my skills of comprehending and disseminating English are not THAT bad. It appears he is aware of the discussion but has not participated in it himself, and will look into it in the fullness of time. Our own time on the issue wasn't extensive, actually!

I await his response in the not too distant future. It will be interesting...

 

[Zep]

May I make a suggestion? As long as you try to analyze the problem from Zeno's perspective, it will always be a paradox. I'd suggest abandoning that approach. I don't yet know which approach will ding the bell for you, but may I suggest looking at the rule for converting the decimal expansion of rational numbers to their fractional equivalent.

Thanks, I will.

Does the term "for all intents and purposes" mean something here? In which case, I would happily employ it thus:

0.9... for all intents and purposes = 1

 

[patoco12]

His initial comment: This has always been a grey area and subject of much argument.

I don't doubt he said this; but it DOES surprise me. All of my colleagues accept this to be fact -- mainly because we can prove it.

one first needs to understand what is meant by performing the limit calculation, why it is done in the first place.

We really only need to understand WHAT the limit is, not what it is used for. Mathematics are invented (not discovered), so everything has a solid definition.

But infinity is a funny thing so I'll get back to you when I've thought about it some more!

I agree infinity becomes funny when we APPLY Math to something. For example, as Mathematics is our "telescope" on deep portions of the universe, our notion of infinity causes some strange things. But we have defined infinity and we have defined decimal notation and repeating decimal notation. No interpretation is necessary.

Meanwhile, I'm still plunking for an inequality of the series itself, whereas I'm more than happy that the limit of same is indeed unity (as accepted by me originally).

There is more than one way to think of this problem. Try a new approach. You could look up some proven theorems of rational numbers and apply them to our problem. That would be a good way of portraying your point of view without falling into a trap of the "philosophy" of what limits and series are.

Again, if you can come up with two integers A and B such that A/B = .9~ and A != B, then you have a proof that .9~ != 1.

One more thing, don't dismiss the simpler proofs in this thread because of their simplicity.