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#26 2013-03-07 03:03:24

bobbym
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Re: [1 paradox]

It is the same as .3333333... which you already accepted!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#27 2013-03-07 03:07:39

anonimnystefy
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Re: [1 paradox]

Hm, but, you see, I do not allow for repeating 9's after the decimal point. I find that every number has a unique decimal representation that way!


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#28 2013-03-07 03:09:52

bobbym
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Re: [1 paradox]

But you allow for .333333... and .6666666... why stop at .9999999...?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#29 2013-03-07 03:18:34

anonimnystefy
Real Member

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Re: [1 paradox]

Because there is no other way to write the first two. The third is needless.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#30 2013-03-07 03:22:27

bobbym
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Re: [1 paradox]

Not really it also represents 3 x .3333333... and 9 x .1111111..., all of which you agree exist but suddenly when we multiply they disappear like magic?

Last edited by bobbym (2013-03-07 03:22:42)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#31 2013-03-07 03:24:47

anonimnystefy
Real Member

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Re: [1 paradox]

Yes, but those are not decimal representation of that number.

And, they don't disappear. Both of those are 1.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#32 2013-03-07 03:27:47

bobbym
Administrator

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Re: [1 paradox]

They are also digit by digit multiplication. We are allowed to multiply are we not?

.999999999... exits because as you say .33333333... exists.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#33 2013-03-07 03:36:43

anonimnystefy
Real Member

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Re: [1 paradox]

We are allowed to multiply. 3*0.3333...=1.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#34 2013-03-07 03:38:20

bobbym
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Re: [1 paradox]

How do you know that 3 * .3333333... = 1?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#35 2013-03-07 03:51:54

anonimnystefy
Real Member

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Re: [1 paradox]

Because 3*0.333...=3*(1/3)=1.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#36 2013-03-07 03:56:34

bobbym
Administrator

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Re: [1 paradox]

Hmmm, that is because you know and accept that 1 / 3 = .3333333. What would you do for this one?



What fraction is that?

Last edited by bobbym (2013-03-07 03:56:51)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#37 2013-03-07 04:08:07

anonimnystefy
Real Member

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Re: [1 paradox]

It is 1/2071.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#38 2013-03-07 04:08:42

bobbym
Administrator

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Re: [1 paradox]

How do you know that?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#39 2013-03-07 04:09:59

anonimnystefy
Real Member

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Re: [1 paradox]

It was easy finding it.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#40 2013-03-07 04:15:24

bobbym
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Re: [1 paradox]

No it was not. It was easy for your package to find it.

Supposing I gave you one that your package could not get. Let us assume it is that one. Prove that 2701 x that number is one?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#41 2013-03-07 04:27:27

anonimnystefy
Real Member

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Re: [1 paradox]

Well, if I had a package, I would simply divide 1 by 2071 and check to see if it is that number.

Last edited by anonimnystefy (2013-03-07 04:51:27)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#42 2013-03-07 04:36:29

bobbym
Administrator

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Re: [1 paradox]

Did you try that?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#43 2013-03-07 04:51:43

anonimnystefy
Real Member

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Re: [1 paradox]


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#44 2013-03-07 04:59:39

bobbym
Administrator

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Re: [1 paradox]

Hohohohohohohohohoh! That is a good one. Very good!

Ever wonder how wolfram did that? Supposing you had to do it without alpha, could you prove that 2701 x that decimal expansion is 1?

For that matter you have not proved that 3 * .3333333... = 1. What if you did not know that 1 / 3 = .33333333...?

Last edited by bobbym (2013-03-07 05:08:31)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#45 2013-03-07 05:11:38

anonimnystefy
Real Member

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Re: [1 paradox]

Well, I do know that 1/3=0.333... Supposing that I do not is very unrealistic.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#46 2013-03-07 05:18:34

bobbym
Administrator

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Re: [1 paradox]

I am asking for the proof without that knowledge because for the bigger fraction you would only have the repeating decimal not the fraction. Do you think that mathematica knows that fraction offhand?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#47 2013-03-07 05:57:49

bob bundy
Moderator

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Re: [1 paradox]

hi bobbym and Stefy

bobbym wrote:

Supposing I gave you one that your package could not get. Let us assume it is that one. Prove that 2701 x that number is one?

Well it's only a long division.  So given the following I could do it without a computer of any kind:

(i) large sheet of paper (A0 or bigger)

(ii) A pencil and sharpener

(iii) A sufficient incentive to maqke the effort ($1000000 should do it)

smile

Bob


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

#48 2013-03-07 06:10:22

bobbym
Administrator

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Re: [1 paradox]

Hi;

Where I am going with this is simple. Multiplying .333333333333333... by 3 is never going to produce that magical 1. It is going to produce a long string of nines. anonimnystefy gets around that by calling it 1 / 3 and doing rational arithmetic. But what happens when you do not know the rational equivalent of the decimal? He is now forced to do the multiplication



Always the string of nines.

Last edited by bobbym (2013-03-07 06:14:51)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#49 2013-03-07 07:54:01

anonimnystefy
Real Member

Offline

Re: [1 paradox]

That is because you do not have enough digits of precision.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#50 2013-03-07 08:38:27

bob bundy
Moderator

Offline

Re: [1 paradox]

But my point is, you can achieve the same without doing a multiplication.  You do a division instead.  By long D you get all those digits and then the recurring clicks in and you can stop.  No precision problem at all.

Bob


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

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