भगवान को चुनौती देना वाला Ramanujan Paradox | Power of Ramanujan number | Interesting number paradox 

The interesting number paradox is a mathematical paradox that came into existence when two mathematicians G.H. Hardy and Srinivasa Ramanujan were discussing about interesting and uninteresting numbers.
G.H. Hardy told Ramanujan, “The taxicab number 1729 seems uninteresting”. To which, Ramanujan contradicted that it is interesting as it is the smallest number which is the sum of two cubes in 2 different ways.
This paradox attempts to classify the natural numbers into interesting and uninteresting set of numbers and the mathematical proof was given by contradiction.
Suppose we have a set of uninteresting natural numbers but the smallest number in that set would be interesting as it is the smallest number and thus raising a contradiction.
0 is the additive identity.
1 is the multiplicative identity.
2 is the only even prime.
3 is the number of spatial dimensions we live in.
4 is the smallest number of colors sufficient to color all planar maps.
5 is the number of Platonic solids.
6 is the smallest perfect number.
7 is the smallest number of sides of a regular polygon that is not constructible by straightedge and compass.
8 is the largest cube in the Fibonacci sequence.
9 is the maximum number of cubes that are needed to sum to any positive integer.
10 is the base of our number system.
The interesting number paradox asks (basically) what is the smallest positive integer which is uninteresting? So, for example, 1 is interesting because it’s the multiplicative identity. 2 is interesting because it’s the smallest and only even prime number. 3 is the smallest odd prime… 6 is a perfect number… 10 is the fourth triangular number… 1729 is the smallest number which can be written as the sum of two cubes in two different ways etc. What’s the smallest number for which we cannot find something interesting to say about it? Let’s start by putting some limits on what we mean by interesting: say we have to describe the number in 100 words or less for it to be interesting. (Otherwise all numbers are interesting). So since there are a finite number of words, there are a finite number of 100 word descriptions. This number is astronomically large, but it’s finite. So there must be some numbers… in fact an infinite number… which cannot be described in 100 words or less. And since the integers are well ordered under the natural ordering, there must be a smallest number which is not interesting.
But suppose that x is “the smallest number which cannot be uniquely described in under 100 English words”. Doesn’t that make x interesting? We described it uniquely in under 100 words so by our definition x IS interesting. Thus, a paradox.
This paradox falls into the category of first order propositional logic paradoxes. “This sentence is false” or Russel’s paradox “the set of all sets which do not contain themselves”
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भगवान को चुनौती देना वाला Ramanujan Paradox | Power of Ramanujan number | Interesting number paradox
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