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

[Jeremy Bowers]

On Sat, 30 Oct 2004 16:06:04 -0400, Brian van den Broek wrote:
> 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.)

*shrug* Can't say I get worked up over the difference there. Regardless,
you "can't" write "3". (Of course you can define it, but that's true of
everything.)

> 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.)

Yeah, that would be right. Couldn't recall the exact name.

>> 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 :-)

Gonna nit pick myself here: "Most people". I think adding Philosophers and
dilettantes and the rare electrical engineer isn't likely to change the
"most". 

> 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 :-|

Graduate level. And many of the grads hated it. There is a chasm between
the average Comp. Sci. student and the average professor; it isn't so bad
at the grad level but it is still there. I'm not sure if it's worse than
most disciplines, but I am inclined to believe it is, since Comp Sci
typically can't really work out if it is math or engineering (wide
consensus is that while there are scientific aspects to it, it probably
shouldn't have it in the name), and there are, in my experience, fairly
clean divisions of each student and professor into one camp or another. I
was one of the exceedingly rare students who could do both quite well, and
freely translate between them.