07/30/2009, 11:40 PM
(07/30/2009, 06:21 PM)mathamateur Wrote: of course -oo and +oo is a number. Are you saying 0 is not a number? its 1/oo and -1/oo. you can make -oo a number since its 0-oo and 0-delta oo.
tell me your thoughts
the infinities are not (normally) considered numbers (that you can treat like ordinary numbers) because if you do, you lose some important algebraic properties. There are extensions of real and complex numbers to include infinity/ies. The "extended number line" has the positive and the negative infinity you want. The "real projective line" tapes the two infinities together to make it one infinity. But you still cant do infinity - infinity. Also you don't know if 1/0 is positive or negative unless there are both positive and negative zeros. Actually it's neither. infinity doesn't behave like numbers all the time, so mathematicians just like to be careful.
But for a simple operation like deltation, it may be useful to treat it like a "zerative" identlty. Some info on limiting values of zeration may be needed tho.