Interesting-number-paradox-Wikipedia #

Interesting number paradox - Wikipedia #

Created: February 2, 2020 7:56 AM URL: https://en.wikipedia.org/wiki/Interesting_number_paradox The interesting number paradox is a semi-humorous paradox which arises from the attempt to classify every natural number as either “interesting” or “uninteresting”. The “proof” is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a contradiction. In a discussion between the mathematicians G. H. Hardy and Srinivasa Ramanujan about interesting and uninteresting numbers, Hardy remarked that the number 1729 of the taxicab he had ridden seemed “rather a dull one”, and Ramanujan immediately answered that it is interesting, being the smallest number that is the sum of two cubes in two different ways.

Paradoxical nature[edit] #

Attempting to classify all numbers this way leads to a paradox or an antinomy of definition. [1] The number fitting this definition later became 12407 from November 2009 until at least November 2011, then 13794 as of April 2012, until it appeared in sequence OEIS: A218631 as of 3 November 2012. [citation needed] The mathematician and philosopher Alex Bellos suggested in 2014 that a candidate for the lowest uninteresting number would be 247 because it was, at the time, “the lowest number not to have its own page on Wikipedia”. [3] Untitled

See also[edit] #

• Church–Turing thesis
• Gödel’s incompleteness theorems
• Grelling–Nelson paradox
• Kleene–Rosser paradox
• List of paradoxes
• Richard’s paradox
• The Penguin Dictionary of Curious and Interesting Numbers
• Unexpected hanging paradox

Further reading[edit] #

• Gardner, Martin (1959).