On 16-11-2009 17:15, Invisible wrote:
> Darren New wrote:
> 
>> Which just goes to show the problem I have with 90% of all 
>> matehmatical notation. It's so utterly inconsistent that even 
>> something like (f(f(x))) is ambiguous.
> 
> Several millennia of mathematical discoveries, all made by different 
> people in different places, and apparently several of them discovered 
> the same or similar things, but gave them different names - or gave them 
> names which clash with existing but inrelated things they didn't know 
> about.
> 
> Just for giggles: how many meanings can you find for "normal"?
> 
> There's the normal distribution, normal vectors, a normed space...

Wednesday I have again an opportunity to give my talk on deriving 
programs from specifications. One of the things I mention is that the 
humble '=' has at least five and possibly more meanings depending on 
context, interpretation, and the type op the object that it is applied 
to*. And I will not even mention that the general use is inconsistent in 
the context of A=B+C where A,B,and C are matrices. Here '+' is 
pointwise, while '=' has an implicit summation**. As far as I know there 
is not even an generally accepted symbol to express pointwise equality. 
I know of people that try the opposite and make the summation explicit, 
but that breaks most of other mathematical uses.


* equivalence, equality, definition, EXNOR, assignment and perhaps one 
or more that don't have names. The type plays a role in A=B=C which is 
OK if they are all booleans (or A or C is) but not if they are all 
integers. In A=5 it can be an expression of equality, if A was undefined 
it can be a binding/assignment, but it can also be a boolean that is 
false everywhere except at 5.

** See also the concept of '=' in OO languages. Are two objects the same 
if all fields are the same?

Post a reply to this message