Those of you who've had the
Theorem: There are no uninteresting natural numbers.Yeah, it's a pretty stupid joke. It goes over slightly better in class.
Proof: Notice that the first several natural numbers have interesting properties. 0 is the additive identity; 1 is the multiplicative identity; 2 is the first prime; 3 is the first odd prime; 4 is the first composite number; 5 is the first number which is the sum of two different primes, and so on. So, suppose by contradiction that there are uninteresting natural numbers. Let U be the set of uninteresting natural numbers; as a subset of the natural numbers, by the Well-Ordering Principle, U has a least element n. But the smallest element of a set is by definition interesting, so n cannot exist. Thus, U cannot exist, and all natural numbers are interesting.
Anyways ... the web page linked above is one person's attempt to find the interesting properties of all numbers between 0 and 9999. Not every number has a property yet ... but an amazing number do have.
