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

Andrea Griffini agriff at tin.it
Sun Oct 31 09:30:14 CET 2004


On Sat, 30 Oct 2004 16:06:04 -0400, Brian van den Broek
<bvande at po-box.mcgill.ca> wrote:

>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.)

Also the representation used in that context is normally
"0,s0,ss0" or a similar one; anyway using TWO symbols.

In math, or anywhere you need precision, it's important
to weight the words; I said "positional" and normally the
unary counting method is not considered "positional".
There are a lot of methods for representing numbers, both
historically used (roman, for example) or just theorically
possible. When the word "base" is used the assumption is a
positional system; and 1 cannot be used as base in a
positional system. More to the point the objection that
the code that Alex wrote didn't handle "unary" counting
is IMO quite pointless as that counting system is not
more related to the positional than the ancient roman
counting system.

Of course anyone can give the the words whatever meaning,
it just gets harder to communicate.

Also, if ones really wants to support another different
number representation system after a generic positional
I would prefer the roman one, that's still used nowdays.

Andrea


--
"When I use a word," Humpty Dumpty said, in rather a
scornful tone, "it means just what I choose it to
mean—neither more nor less."



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