100 mathematicians and 1 sequence of real numbers

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Bertha
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100 mathematicians and 1 sequence of real numbers

Postby Bertha » Tue Jul 23, 2013 5:34 pm

As a fan of brain teasers, I've never come across one quite like this one. It is fairly remarkable and certainly teases my brain.

It involves an axiom in mathematics called the axiom of choice, so if you're serious about trying to solve it, you may want to read the wikipedia article on the axiom of choice.

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Gord
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Re: 100 mathematicians and 1 sequence of real numbers

Postby Gord » Wed Jul 24, 2013 2:02 am

I can't even understand the set-up!

"For any natural number n, all 100 boxes labeled n (one in each room) contain the same real number."

There are 100 boxes in each room? Or one box in each room? Or an unknown number of boxes in each room? And they're labeled with the number that they contain?


...ow :befuddled:
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Bertha
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Re: 100 mathematicians and 1 sequence of real numbers

Postby Bertha » Wed Jul 24, 2013 2:10 am

In each room there are boxes labeled with the natural numbers 1,2,3,... So there are infinitely many boxes in each room, and as strange as it may seem, this is often referred to in math as 'countably many,' because there are as many boxes as there are 'counting numbers,' that is, the numbers 1,2,3,...

Now, since there are 100 rooms, there are actually 100 boxes labeled with the number 7, one 'box number 7' in each of the rooms. Similarly, there are 100 boxes labeled with the number 198, one in each of the 100 rooms. And, it just so happens that all boxes labeled 7 have the exact same number inside. Similarly, all 100 boxes labeled 198 have the exact same number inside as well. In other words, the rooms are identical with respect to the boxes and the numbers inside of them.

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Gord
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Re: 100 mathematicians and 1 sequence of real numbers

Postby Gord » Wed Jul 24, 2013 3:28 am

Oh.




:|
"Knowledge grows through infinite timelessness" -- the random fictional Deepak Chopra quote site
"You are also taking my words out of context." -- Justin
"Nullius in verba" -- The Royal Society ["take nobody's word for it"]
#ANDAMOVIE

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Kaepora Gaebora
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Re: 100 mathematicians and 1 sequence of real numbers

Postby Kaepora Gaebora » Thu Jul 25, 2013 4:16 am

I feel dumb.

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octopus1
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Re: 100 mathematicians and 1 sequence of real numbers

Postby octopus1 » Thu Aug 01, 2013 9:50 pm

Well it's not impossible. The premise is too neatly outlined.

I can't think of a valid function that would result in a win though :S

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