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Comment by falcor84 | Hacker News Reader

https://en.wikipedia.org/wiki/Interesting_number_paradox

Like the Original Sin entered the Garden of Eden through the Serpent, mutable state breaks the time-invariant perfection of mathematics through the idea of interestingness, since it's clear the least interesting things only remain so until someone notices.

Well, that is about the question which is the most uninteresting number. And the paradox that - whichever number it is - this attribute makes it interesting.

But since we are not looking for the most uninteresting number, but the most interesting one, we do not have to fight with issues of that calibre.

True, but you must still contend with your observational influence. Whatever number you crown as "most interesting" will become even more interesting for wearing that crown!

So you must take this duty with extreme care and thoughtfulness, for when you anoint such a number, your action may crystalize it as such for all eternity. Other numbers will have to go further to supplant it.

I know it's a joke, but I still feel like it would be more meaningful if it wasn't so generic that it could kind of apply to anything. Like, there's nothing specific to numbers about the idea that the least-"interesting" item in some set is itself interesting for possessing that property.

Then let's see who manages to write the least interesting comment in this thread.

The way I understood it, this formulation relies on induction on the natural numbers.

Because it's numbers, which are sortable, you can ask which is the least member of a set. If a set of positive numbers doesn't have a least member, does the set exist?

There's a similar paradox which asks what the smallest number that can't be defined in fewer than thirteen words.

There must be some number, right? For instance, 7603201560, or "seven billion six hundred and three million two hundred and one thousand five hundred and sixty" seems to require 16 words. Maybe you can shorten it by removing the "ands," but I can come up with a longer number.

But if there were such a number, then couldn't we describe it as "the smallest number that can't be defined in fewer than thirteen words?" And then it just got defined in fewer than thirteen words. So it can't really be a member of that set.

So does the set have any members?

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