On 17-11-2009 10:20, Invisible wrote:
>> * equivalence, equality, definition, EXNOR, assignment and perhaps one 
>> or more that don't have names.
> 
> I'm failing to see how equivalence and definition are different. 

If you say that f(x)=x^2+4x+1 then that is an equivalence, because that 
will allow you to conclude say that x^2+3x+3=f(x)-x+2. If, however, this 
is the first time you mention f(x) it is probably meant as it's 
definition. Difference is subtle and has mathematically no significance, 
but it feels different. Just as x=5 seen as a statement that the 
solution to the problem is when you take x to be 5, feels different from 
viewing = as a boolean function of two variables, x and 5.

>(I know  some people use the triple-line symbol for this though.)
> 
> The main confusion is between assignment and equality, generally. 

That is why most languages have separate symbols for both meanings (and 
why I am advocating imperative languages without assignment).

> Or, in mathematics, between a test for equality and a statement of equality.

Can you give an example of that?

>> ** See also the concept of '=' in OO languages. Are two objects the 
>> same if all fields are the same?
> 
> You would first have to define the concept of fields being "the same". ;-)

spot on

> Fortunately, in a pure functional language, the question becomes a lot 
> simpler.

Not so sure about that. Anyway even if that would be the case it doesn't 
solve the 'problem' that in real life you have multiple views to look at 
an equation.

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