
The smallest uninteresting number - munin
http://www.johndcook.com/blog/2012/12/31/fuzzy-logic/
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Sniffnoy
This isn't a paradox. It's simply a proof that all natural numbers are
interesting, if we accept the premises. We shouldn't accept the premises,
because there really is a real paradox lurking around the corner, but this
isn't it.

The paradox occurs when we replace "natural number" by "ordinal". Then the
same line of reasoning demonstrates that all ordinals must be interesting. But
surely there can only be countably many interesting ordinals! (Because
"interesting" is really code for "definable".) Which shows what the real
problem in the premises were -- we failed to distinguish between definable in
some particular theory and definability in the meta-theory.

See: <http://en.wikipedia.org/wiki/Berry_paradox>

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nathell
Theorem: All natural numbers are boring.

Proof (by contradiction): Assume the set of non-boring natural numbers is
nonempty, so it must have a smallest element. Call it x. So what? _yawn_

QED

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JoeAltmaier
2013 is sort of interesting - first year with non-duplicate digits since 1987

~~~
dexen
While interesting, that is property of _decimal notation_ rather than the
integer number itself. In hexadecimal notation, 2013 is the first (since 2007
-> 0x7d7) _with_ duplicate digits ;-)

    
    
        1987 -> 0x7c3
        1988 -> 0x7c4
        1989 -> 0x7c5
        ...
        2007 -> 0x7d7
        2008 -> 0x7d8
        2009 -> 0x7d9
        2010 -> 0x7da
        2011 -> 0x7db
        2012 -> 0x7dc
        2013 -> 0x7dd

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cowpewter
Perhaps this is the point of the original article, but couldn't one say that
the actual "smallest uninteresting number" is actually the second smallest
uninteresting number? The first smallest uninteresting number is only
interesting by virtue of being otherwise uninteresting, but once we have a
second number that is only interesting by virtue of being uninteresting, it's
no longer a novelty to be uninteresting. So it's legitimately uninteresting.

~~~
praxulus
So it's the first legitimately uninteresting number, that's pretty interesting
if you ask me.

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javajosh
Uh, the smallest uninteresting number is clearly 14.

~~~
DanBC
"14 is the smallest even number n with no solutions to φ(m) = n."

(<http://www2.stetson.edu/~efriedma/numbers.html>)

~~~
asimjalis
According to this table 391 is the smallest uninteresting number.

~~~
vacri
Some of those are a bit of a reach. "57 is 111 in base 7"? 111 in base 10
isn't interesting because it's a sequence of the same digit. "22 is the number
of partitions of 8" is an interesting thing about 8, not 22, I would argue,
since it's not a property inherent to 22.

Mind you, 22 is a sequence of the same digit, so I guess that counts as
interesting for some reason...

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lubos
relevant: [http://www.njohnston.ca/2009/06/11630-is-the-first-
uninteres...](http://www.njohnston.ca/2009/06/11630-is-the-first-
uninteresting-number/)

