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: defence...

[ciphergoth.livejournal.com]

To add to what Anne's said:

You can assign the symbols in "infinity = infinity + 1" meanings such that the whole expression is meaningful and true[1], but then the "+" symbol becomes extremely ill-behaved. In particular, it no longer has a sister called "-" that does what you expect, so you can't just "subtract infinity from both sides" and expect it to work. Infinity is a tricky bugger like that.

But when Anne proves that 0.9(rec) = 1, she's using all the normal meanings of the symbols, so they're extremely well behaved - when we refer to the real numbers as a "field", it's another way of saying that all these symbols are incredibly well behaved! And so her proof is sound.

[1] in more than one way - I know of two! One of which is so weird that 1 + infinity = infinity but infinity + 1 > infinity!

interesting shit

[ajva.livejournal.com]

This is, indeed, where loads of interesting shit starts happening. I have only a vague idea about it, but am determined to read more once I have done with categorising wallpaper patterns and colouring in dodecahedra etc.