From: utzoo!decvax!duke!unc!mcnc!uvacs!mac Newsgroups: net.math Title: nonscience Article-I.D.: uvacs.406 Posted: Mon Jan 31 12:51:19 1983 Received: Wed Feb 2 05:52:51 1983 More Notation A^B is the cardinality of the functions B->A. 2^B is card(characteristic functions B->2), which correspond to the subsets of B (like the Pascal representation of sets). Apparently the use of Beth cardinals is peculiar to one author. The usual notation for the continuum is German script c, or just c if that's all you can afford. Puzzle What's yellow and neither true not false? Fun with ... Proof that the universe is two's complement (as opposed to one's complement or sign-magnitude). [Gosper, Item 154, MIT- AI-239] let x =: ...111111 then x+x = ....111110 = x-1 2*x = x-1 so x = -1, characteristic of two's complement machines Be careful of arithmetic with "...".