# Numeric literals in other than base 10 - was Annoying octal notation

Steven D'Aprano steve at REMOVE-THIS-cybersource.com.au
Thu Aug 27 03:34:10 CEST 2009

On Wed, 26 Aug 2009 10:58:12 -0700, Mensanator wrote:

>> But I certainly wouldn't call it "binary", for fear of confusion with
>
> 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
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