Kalman Noel
Achim Schneider wrote:
Actually, lim( 0 ) * lim( inf ) isn't anything but equals one, and the anything is defined to one (or, rather, is _one_ anything) to be able to use the abstraction. It's a bit like the difference between eight pens and a box of pens. If someone knows how to properly formalise n = 1, please speak up.
Sorry if I still don't follow at all. Here is how I understand (i. e. have learnt) lim notation, with n ∈ N, a_n ∈ R. (Excuse my poor terminology, I have to translate this in my mind from German maths language ;-). My point of posting this is that I don't see how to accommodate the lim notation as I know it with your term. The limit of infinity? What is the limit of infinity, and why should I multiplicate it with 0? Why should I get 1?
n * n = 1 where lim lim n -> 0 n -> oo You don't get 1, you start off with it. If you want to find the area of a function, you slice 1^2 into infinitely many parts and then look how much every single slice differs from lim( 0 ) * 1, all that lim( inf ) many times. When you've finished counting pebble, you know how to scale this 1^2 to match it with your "normal" value of 1. n = 12 n = 1 * n now, 1 is twelve. QED: The wrath of algebra. "One" as a pure concept is a very strange beast, as it can mean anything. Like, if you take something and try to understand it by dividing it successively into infinitely many parts, the meaning of each part will approach zero, as you don't change the thing you're analysing but the nature of your lenses. If you ever want to watch a zen master frowning or despair, tell him exactly that. -- (c) this sig last receiving data processing entity. Inspect headers for past copyright information. All rights reserved. Unauthorised copying, hiring, renting, public performance and/or broadcasting of this signature prohibited.