On Wed, 26 Aug 2009 10:58:12 -0700, Mensanator wrote: >> But I certainly wouldn't call it "binary", for fear of confusion with >> radix-2 binary. > > That's my point. Since the common usage of "binary" is for Standard > Positional Number System of Radix 2, it follows that "unary" is the > common usage for Standard Positional Number System of Radix 1.
Er, no, that doesn't follow. There is no such thing as a radix-1 positional number system -- it just doesn't work. In any case, unary is the standard term for what I'm discussing: http://en.wikipedia.org/wiki/Unary_numeral_system although Mathworld doesn't seem to know it. > That's VERY confusing since such a system is undefined. Base-1 positional system is defined, it just doesn't work. You would have to write a number by the sum of 0*(1**i), which clearly doesn't get you very far. Positional unary is only capable of representing zero, and no other numbers, which is even less useful than unary, which at least can be used for counting positive numbers, addition and subtraction, and even has a use in Elias gamma coding. > Remember, common usage > does not necessarily properly define things. Saying simply "unary" > sounds like you're extending common usage beyond its proper boundaries. You're reasoning by analogy: "binary" means "positional number system with radix 2", "decimal" => radix 10, etc, so "unary" => radix 1. That's a reasonable heuristic to follow, but it can fail, because even in mathematics, names for things don't necessarily follow such patterns perfectly. Because the radix 1 positional system can't work and therefore doesn't exist, the name "unary" is available, and has been taken to describe a number system which counts by tally marks. -- Steven -- http://mail.python.org/mailman/listinfo/python-list
