[OT] Re: "number-in-base" ``oneliner''

Brian van den Broek bvande at po-box.mcgill.ca
Sat Oct 30 22:06:04 CEST 2004


Hi all,

warning: off topic nitpicking below!

Jeremy Bowers said unto the world upon 2004-10-30 13:29:
> On Sat, 30 Oct 2004 12:12:36 +0000, Andrea Griffini wrote:
> 
>>You can't count using base 1 with positional systems.
> 
> 
> Well, you can, sort of. You end up with the integers, obviously, and the
> result has a rather striking resemblance to the modern foundations of
> number theory, in which there is only one number, 0, and the "increment"
> function which returns a number one larger. If you want three, it is
> expressed increment(increment(increment(0))), which is rather similar to
> the base-1 number "111". 

I take it you didn't mean 0 was the only number, but rather the only 
primitive number. (Alternatively " '0' is the only individual constant" 
in the cant I prefer.)

I am also surprised to see "increment" -- I come to that material with 
working in Philosophy of Mathematics and Logic, but almost every 
presentation I have ever seen uses "successor". (I'm going off of 
philosophical and mathematical logic presentations.)

I do so wish that terminology is the whole area would just stabilize 
already!

> 
> Zero in this system would probably be a null string, making increment this:
> 
> def increment(number):
> 	return "1" + number
> 
> (And abracadabra, I'm back on topic for the newsgroup, albeit tenuously :-) )
> 
> Some people say base 2 is the most natural base in the universe. But you
> can certainly make a claim for base 1, based on its correspondence to
> number theory, from which we build the rest of math. (Most people never
> dig this deep; it was one of my favorite classes in Comp. Sci., though,
> and we're probably the only people other than mathematicians to offer the
> course.)

I've never taken a single comp. sci. course, so I will both claim and 
commit disciplinary bias: serious undergrad logic/foundations of maths 
courses do happen in Philosophy, too :-)

On the other hand, I'm a bit surprised that these things get taught in 
comp. sci. This past summer when teaching Intro to Logic, I encountered 
at least one fourth-year comp. sci. student who had no idea what an 
axiomatic system was :-|

print "We now return you to your usual programing"

Best to all,

Brian vdB




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