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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

1 paradox reborn

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.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: 1 paradox reborn

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


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: 1 paradox reborn

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


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: 1 paradox reborn

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


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: 1 paradox reborn

progress for whom?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: 1 paradox reborn

The world and the forum.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: 1 paradox reborn

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


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: 1 paradox reborn

Because there are not that many jerks on math forums.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: 1 paradox reborn

but they are basically good and fun to be around


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: 1 paradox reborn

Not really. They are abusive.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: 1 paradox reborn

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.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: 1 paradox reborn

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


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: 1 paradox reborn

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: 1 paradox reborn

Hi;

Fortunately, the great majority are good.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,336

Re: 1 paradox reborn

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.

smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 612
Website

Re: 1 paradox reborn

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)


154 books currently added on Goodreads

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

TheTick
Member
Registered: 2012-12-03
Posts: 27

Re: 1 paradox reborn

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)


Spooooon!!!

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: 1 paradox reborn


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,336

Re: 1 paradox reborn

Interesting link, thanks.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: 1 paradox reborn

The American way?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: 1 paradox reborn


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: 1 paradox reborn

I agree wholeheartedly.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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