8 ms·

Any number is remarkable if you're smart enough to find why it's remarkable.

• eythian 6y ago
  And if it's not remarkable, then that is in itself remarkable.
  • forinti 6y ago
    Aren't most transcendental numbers unremarkable?
    • grahamlee 6y ago
      No number is unremarkable. Let's construct the set of all unremarkable numbers. Now, let's construct the sequence of those numbers in order. The first member of that sequence has the remarkable property that it is the smallest unremarkable number. That is remarkable, so remove it from the set. By induction, the set must be empty.
      • jlokier 6y ago
        > Now, let's construct the sequence of those numbers in order. The first member of that sequence Not happening. Sets of numbers do not always have a first in order. Consider the set of unremarkable real numbers > 0 under the regular arithmetic ordering. Which one is first?
      • gnulinux 6y ago
        That doesn't work because real numbers are not enumerable, so you cannot induce over them. That joke "proof" only works for natural numbers and goes like this: Theorem: all natural numbers are interesting * Base case: 0 is interesting because it is the smallest natural number, as well as the identity element of + operation. * Inductive case: Assume the theorem holds for all m, m<n. Take n. If it is not interesting, then n is the smallest non-interesting number. But that's interesting because it's the smallest such number. Therefore it cannot be non-interesting. Therefore theorem holds for n. By induction, we conclude all natural numbers are interesting. QED.
        • jessaustin 6y ago
          ...only works for natural numbers... That proof also works for the rationals with a suitable ordering. Example: 0, 1, -1, 2, -2, 1/2, -1/2, 3, -3, 1/3, -1/3, 2/3, etc....
          • gnulinux 6y ago
            Yes works for all enumerable set (i.e. all sets that have a bijection with natural numbers).
• Vvector 6y ago
  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. https://en.wikipedia.org/wiki/Interesting_number_paradox https://en.wikipedia.org/wiki/Interesting_number_paradox