Interesting number paradox

As Interesting numbers paradox is called in mathematics a paradox that arises when attempting to classify numbers as interesting or uninteresting. Process, we describe a number without any special property as uninteresting number, all other numbers are interesting numbers.

The interesting numbers paradox arises now from the fact that there is a positive in itself, even if not entirely serious evidence which shows that no uninteresting numbers can exist and thus there is only interesting numbers.

Evidence

The short and classic-looking proof by contradiction uses the well-ordering of the natural numbers, which states that any subset of the natural numbers always contains a smallest number.

Suppose there is a nonempty set of uninteresting natural numbers. Then there is a smallest uninteresting natural numbers because of the well-ordering of the natural numbers. This smallest uninteresting natural number is even but especially distinguished by their Minimalitätseigenschaft over all other uninteresting facts and is therefore just no uninteresting natural number. However, this is in contradiction to our assumption that it is an uninteresting natural number. Thus our assumption of the existence of uninteresting natural numbers is wrong, there are only interesting natural numbers.

Anecdotes

GH Hardy called the number 1729 one anecdote as " meaningless ", but was then informed by S. Ramanujan about this being " the smallest natural number [ is ] that can be expressed in two different ways as a sum of two cubes " ( see S. Ramanujan # anecdotes ).

A number can be referred to as "boring" if it is not explicitly found in the On- Line Encyclopedia of Integer Sequences. For a long period of 8795, the smallest number was boring in this sense.