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

defence...

[ajva.livejournal.com]

*sigh*

I knew I shouldn't have started this.

I am indeed talking about "the ordinary real numbers you learn in school". Sorry if I didn't make that clear.

But look, imagine infinity as a package, right? One single package of infinity? You can't change what's in the package, but you can add or subtract the package to anything else.

So you can't say infinity=infinity+1 because you can't add 1 to infinity. That's like slipping a brick into a locked box. But you could put the brick on top of the box. They're still two separate things, though.

You can multiply 0.9(rec) by 10 and that's what it means to shift things one place to the left in this number system. By definition. What you are left with after the decimal point is exactly the same as what you started with, so you can take both away as they are the same thing - the locked box. It neatly gets rid of the problem of mixing up finite and infinite numbers, since you don't have to.

bleurgh maths

Re: defence...

[wechsler.livejournal.com]

Yeah, point. There's no point me sitting here thinking "sums to infinity converge but never meet" when they *do*.

Take it as a mark of just how bored I am today that my mind even tried to make something of that. If people don't answer some emails today I really and going to have to go and club them.

Re: defence...

[ajva.livejournal.com]

Och I know what you mean. Fret not. I think you're just thinking too much, to be honest. Isn't that probably a good thing? ;o)

Re: defence...

[wechsler.livejournal.com]

No. It makes my brain hurt ;)

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.

locked box

[ajva.livejournal.com]

No. Bad analogy. It's much more like adding a drop to the ocean. The ocean's still the ocean, and the drop has disappeared.

Excuse me but I had to say that. :o)