
Numbers Aplenty - msvan
http://www.numbersaplenty.com/
======
jschulenklopper
See:
[http://en.wikipedia.org/wiki/Interesting_number_paradox](http://en.wikipedia.org/wiki/Interesting_number_paradox)

'The paradox states that all natural numbers are interesting. The "proof" is
by contradiction: if there exists a non-empty set of uninteresting numbers,
there would be a smallest uninteresting number – but the smallest
uninteresting number is itself interesting because it is the smallest
uninteresting number.'

~~~
ggchappell
But -- it's interesting in a rather different way.

BTW, I once decided that the smallest uninteresting number is 34.

Alas, I don't recall my exact reasoning.

~~~
jschulenklopper
> I once decided that the smallest uninteresting number is 34.

Doesn't that make 34 interesting? :-)

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LeonM
I love it, already learned some new stuff!

One comment though: the background almost made my eyeballs explode...

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zyx321
In reply to a dead comment: The most common definition of natural numbers is
"positive integers." I do agree that 0 is important enough that it would have
merited a mention at least.

~~~
ot
It is somewhat controversial: according to Wikipedia

    
    
        There is no universal agreement about whether to include zero
        in the set of natural numbers. Today some textbooks,
        especially college textbooks, define the natural numbers to
        be the positive integers {1, 2, 3, ...}, while others,
        especially primary and secondary textbooks, define the term
        as the non-negative integers {0, 1, 2, 3, ...}.
    

Among mathematicians, the most common (by far) definition is the one given by
Peano axioms, which include 0. Including 0 is very convenient for a number
(pun intended) of reasons, for example it makes the naturals a monoid, and it
is easier to define the integers.

~~~
OscarCunningham
I'm not sure if it is more common to say that 0 is a natural number. There's a
math.stackexchange thread about this which seems to have equally many people
saying that each is the more common one.

[http://math.stackexchange.com/questions/283/is-0-a-natural-n...](http://math.stackexchange.com/questions/283/is-0-a-natural-
number)

(I count 4 people saying {1,2,3,...} is more common vs 3 saying {0,1,2,...} is
more common. I also notice that N_0 is used by both sides to refer
"unambiguously" to the convention of the other side.)

In my experience {1,2,3,...} is used more in number theory, and {0,1,2,...} is
used more in logic.

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benjamta
Absolutely love it - real great way to explore how all numbers are uniquely
interesting.

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zsiciarz
This can be helpful in Project Euler challenges.

~~~
oxymoron
Another useful site for that purpose is the Online Encyclopedia of Integer
Sequences ([https://oeis.org/](https://oeis.org/)).

A pretty successful strategy for "cheating" at Project Euler is to implement a
brute force solution to get the first few numbers out of a sequence and look
it up in OEIS. If you're lucky, they've already listed a closed form
expression for calculating the sequence at an arbitrary index. Drop the
expression into your code, and you end up with something that tends to be
orders of magnitude more efficient.

Obviously it depends on the structure of the exercise, but it's somewhat
surprising how far it can take you.

~~~
troymc
Some of the OEIS sequences originated with Project Euler problems, so this
strategy is closer to cheating than you might think.

