A question of numbers (one for the maths fans)

You try teaching that to a bunch of argumentative public school boys or an argumentative constructivist for that matter Edited by cavediver, : No reason given.

ACtually, riVeRraT has a point. You have not demonstrated that the entities you are attempting to subtract exist. And in constructivism, they don't.Not that I'm even remotely a constructivist, but it should be recognised.

Good point.Mathematics deals with far more than the usual numbers (an representations of numbers) that we meet in everyday experience. It is more the logical manipulation of symbols, some of which relate to the numbers of our experience. Some symbols appear to have no correspondance to our experience, but certain manipulations bring them back to more everyday objects.Take for example i, the sqrt of -1. It has no real (everday) meaning as you would understand it, except that i^4 = 1, which ties it down to things we can understand. Similarly with the infinite strings of digits that make up recurring decimals and irrational numbers.

Hmmm, I'm not sure of your logic there. You can simply define the symbol .999999... to be 1, but that sort of defeats the object. 1 divided by 3 yields .3333333..., and as a physical (constructable) process never yields the precise 1/3. We would like to imagine the process continuing to infinity to make the answer precise and then treat these infinite strings as simple continuations of the finite decimals, obeying the same operations. One must then ensure that these infinite strings remain consistent under these operations.Fortunately, they are But the constructivist will never believe you becasue you can never produce one! One can never think about maths too much

e^iΠ+1=0 please Though could this be the first mention of Euler's Identity at EvC? Hmmm, and 100 posts in and I don't think anyone has advanced beyond this yet

Yes, but the direction matters It's not the typesetting, it's teaching formal mathematics to an engineer pearls before swine, teaching pigs to sing, etc

Give him some slack, it's a damn site shorter proof than Godel's