Monday, October 27, 2003

Special Numbers

I saw this link on Green Fairy's linklog and thought I'd draw your attention to it, too.

It's a list of numbers that have distinctive facts, such as 1980 being the number of ways you can fold a 2x4 rectangle of stamps. Some of the facts are highly mathematical and some aren't but it is an interesting read if you have a weird fascination with numbers like I do.

It's also reminded me of an illustration of proof by contradiction: Proof that all numbers are special. We can see (from the website above) that some numbers have unique 'special' properties, i.e. properties that no other number has. Lets assume that there are some numbers that are completely unremarkable and have no special properties. Within this list of 'normal' numbers there will be one number that is lower than all of the rest and hence is the lowest 'normal' number, which is a property that no other number can have. But this means the number is special hence our assumption is incorrect and all numbers are special.

Of course, this isn't a real mathematical proof because of the very vague definitions of special and normal. It does, however, show how elegant mathematical argument can sometimes be. That you can start of from a single assumption and, merely by following all the logical implications of that assumption, prove it to be untrue is quite beautiful.

But then I'm a maths geek.

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