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 "...".