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I remember reading that 'the next number in a sequence of numbers can be anything. It is all about finding the a relation between previous numbers such that the required number becomes next in sequence'.

For e.g: take the sequence 3,5,7...

  1. The next number can be 9, if we look at the sequence as A.P with common difference of 2.
  2. The next number can be 11, if we look at the sequence as sequence of prime numbers...

Basically it can be anything, if we can think of a relationship between the numbers...

I can't remember the name of the paradox. Can somebody help me?

Thanks, tecMav.

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    I wouldn't call it a paradox - it's a fact. I can fit a polynomial, for example, given a finite number of points. Add another point, I can still fit a polynomial (of higher degree if the new point isn't on the old polynomial).2012-10-30
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    http://en.wikipedia.org/wiki/Lagrange_polynomial2012-10-30
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    What is the next number in the sequence $0,1,0,1,0,1,\dots$? Actually, it is $7$, I asked my colleagues in turn how many children they had. What is the next number in the sequence $1,2,3,4,5,6,7,8,9,10,11,12,\dots$? It is $1$, I have been clock-watching.2012-10-30
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    Thanks for the replies. But this wasn't the answer I was looking for. The statement I am referring to does not deal with finding the correct next number in sequence. All it says is "it is possible that the next number can be anything. All you have to do is find a reason to fit that number into the sequence'. For e.g, what is the next number in sequence 3,5,7.. It can be 9 based on fact that the difference between numbers is 2, or it can be 11, if you go by treating them as sequence of odd numbers...so if you can find a apt reasoning the next number can be anything...2012-10-31
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    That one would need to *find a[n] apt reasoning* to allow some specific value of the next number is a misconception of what a *sequence* is. (In this respect, while exact, the argument that there exists a polynomial fitting the next value, whatever this next value is, might be misleading, in the end.)2012-10-31
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    Maybe you want to read about "Lawlike and lawless sequences", "Random Sequences" and "Choice Sequences" to find your paradox name. However, those terms refer to solid facts.2012-11-01

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