1 paradox reborn

Agnishom · 2014-02-08 22:37:11

Hello there, I just made this thread because I am too bored that we do not have anymore people who tell us that 0.999... ≠ 1. Since, I really want those days back,

0.999... ≠ 1

because I said so.

bobbym · 2014-02-08 22:49:10

Do you want to give up the summation of a geometric series?

Agnishom · 2014-02-09 05:02:35

I do not know. I just made this up because no one else was doing it

bobbym · 2014-02-09 05:03:32

I would say the fact that there are no more posts like that is progress!

Agnishom · 2014-02-09 05:06:25

progress for whom?

bobbym · 2014-02-09 05:07:28

The world and the forum.

Agnishom · 2014-02-09 05:13:05

Why aren't there more closed threads and banned users?

bobbym · 2014-02-09 05:14:30

Because there are not that many jerks on math forums.

Agnishom · 2014-02-09 05:17:05

but they are basically good and fun to be around

bobbym · 2014-02-09 05:18:26

Not really. They are abusive.

anonimnystefy · 2014-02-09 18:13:14

The thing is that, fortunately, we do not get to see the ad hominem attacks, since most are moderated. What's left of their posts seems really funny, because they give themselves huge accomplishments.

bobbym · 2014-02-09 20:18:40

Yes, to the people responsible for the forum quality these guys are hardly funny or entertaining.

anonimnystefy · 2014-02-10 02:21:15

I cannot begin to imagine it! Thanks for keeping the forum clean!

bobbym · 2014-02-10 02:25:53

Hi;

Fortunately, the great majority are good.

Bob · 2014-02-11 04:39:23

hi Agnishom,

I did say, in another thread, that I would try to give the Shilov proof that 0.9999recurring doesn't exist.

It has been a struggle for me and what follows may not be correct, so I'll apologise now.

Firstly, I couldn't read the small mathematical text on my Kindle. But the nice people at Kindle HQ suggested an app. that means I can read it on my laptop. That helped a lot.

But the relevant section is well on through the first chapter and you only want a small bit. So, could I condense, omit and edit in order to get to where you want? Here's my attempt:

Let r = 0.99999 recurring.

r ∈ [0.9,1) That is r lies in the half open region bounded by 0.9 and 1 but is strictly less than 1.

Similarly, r ∈ [0.99,1) and r ∈ [0.999,1) etc.

So r is in the intersection of all these regions.

But it is a property of the real numbers that, for any two reals, a and b, you can always find a value between them.

So the half open regions cannot have a non empty intersection.

Therefore, r cannot exist.

You may not like this, but it seems to be a requirement for a consistent real number theory. And it is not without precedent. He has already, earlier, shown that 0 has no multiplicative inverse, which is why you mustn't divide by zero.

I think that's it. I don't claim that's how he puts it nor that I like it but there you are. You could always read the book yourself.

Meanwhile, if he is right, then it follows that any discussion of r is meaningless.

Bob

Nehushtan · 2014-02-11 06:37:53

bob bundy wrote:

Let r = 0.99999 recurring.
r ∈ [0.9,1) That is r lies in the half open region bounded by 0.9 and 1 but is strictly less than 1.
Similarly, r ∈ [0.99,1) and r ∈ [0.999,1) etc.
So r is in the intersection of all these regions.
But it is a property of the real numbers that, for any two reals, a and b, you can always find a value between them.
So the half open regions cannot have a non empty intersection.
Therefore, r cannot exist.

This is actually a proof by contradiction that r ≥ 1. In other words the assumption that r < 1 leads to the absurdity that r does not exist.

By the exact same method, you can prove by contradiction that r > 1 is also impossible.

Suppose r > 1. Then r ∈ (1, 1.1], r ∈ (1, 1.01], r ∈ (1, 1.001], and by the same argument it will be found that r does not exist.

Conclusion: If r exists, then r = 1.

Last edited by Nehushtan (2014-02-12 01:22:06)

TheTick · 2014-03-12 15:29:32

What is .99999 recurring + .33333 recurring if .99999 recurring does not equal 1?

Edit- I have no idea btw...

Last edited by TheTick (2014-03-12 15:38:38)

Agnishom · 2014-05-08 17:53:12

http://mathwithbaddrawings.com/2013/08/ … s-forever/

Must read

Bob · 2014-05-08 19:07:17

Interesting link, thanks.

Bob

bobbym · 2014-05-08 20:59:38

The American way?

Agnishom · 2014-06-06 14:02:39

http://forums.xkcd.com/viewtopic.php?f=17&t=14321

bobbym · 2014-06-06 19:56:06

I agree wholeheartedly.

Math Is Fun Forum

#1 2014-02-08 22:37:11

1 paradox reborn

#2 2014-02-08 22:49:10

Re: 1 paradox reborn

#3 2014-02-09 05:02:35

Re: 1 paradox reborn

#4 2014-02-09 05:03:32

Re: 1 paradox reborn

#5 2014-02-09 05:06:25

Re: 1 paradox reborn

#6 2014-02-09 05:07:28

Re: 1 paradox reborn

#7 2014-02-09 05:13:05

Re: 1 paradox reborn

#8 2014-02-09 05:14:30

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#9 2014-02-09 05:17:05

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#10 2014-02-09 05:18:26

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#11 2014-02-09 18:13:14

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#12 2014-02-09 20:18:40

Re: 1 paradox reborn

#13 2014-02-10 02:21:15

Re: 1 paradox reborn

#14 2014-02-10 02:25:53

Re: 1 paradox reborn

#15 2014-02-11 04:39:23

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#16 2014-02-11 06:37:53

Re: 1 paradox reborn

#17 2014-03-12 15:29:32

Re: 1 paradox reborn

#18 2014-05-08 17:53:12

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#19 2014-05-08 19:07:17

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#20 2014-05-08 20:59:38

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#21 2014-06-06 14:02:39

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#22 2014-06-06 19:56:06

Re: 1 paradox reborn

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