this morning

[ajva]

I cycled to the tube station; it saved me 10 mins.

Stef *will* be proud. I wonder if I can get him to study some algebra in return. If he's on a mission to get me ultra-fit, then surely I can be on a mission to cure him of his maths-dunceness?

*ponders*

Comments

Re: aaagh!

[ciphergoth.livejournal.com]

The thing you're looking for when you say "1/infinity" is an infinitesimal. As I said before, there *are* number systems that include infinitesimals, but they have many counterintuitive properties. There are no infinitesimals among the real numbers - for every real number x > 0, there is a perfectly ordinary real number n such that 1/n < x. So either two numbers are exactly the same, or they are some distance apart, with a bit of the number line separating them.

It's clear that there's no distance between 0.9(rec) and 1 - they're the same to within 1/1000 or 1/1000000, or any fraction you care to name. So they're identical.

Or to put it another way, there's something mesmerising about the decimal expansion of 0.999999... that makes people think it must be different from 1. If it were, what would the decimal expansion of 1 - 0.999999... be?

The complex numbers are actually the best behaved numbers of all...