Steven D'Aprano wrote:
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.
Psst. That's a hint.
Googling for "unary number system" ("unary numeral system" just comes up
with endless mirrors of Wikipedia) gives Wikipedia as hit #1. Hit #2 is
from the Institute of Druidic Technology, another hint. The remaining
hits are pretty much people pontificating in discussion groups just as
they are in this one.
Yes, you can define something that works. But it's not the usual
mathematical definition of radix, so if you want to talk about it you
have to disclaim that it's not a proper base and that's you're making up
as you go. But you can't pretend like it's the "obvious" mathematical
meaning just because the usual mathematical meaning doesn't apply, which
is what you seem to be doing.
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