Reinhold Birkenfeld wrote:
>>
>> lambda x,y: x+y*y
>> lambda x,y: y**2+x
>>
>> are essentialy the same functions with different implementations [1].
>
>
> Except that they are not. Think of __pow__, think of __add__ and __radd__.
You know the difference between the concept of a function and it's
infinitely many representations? That's why formal definitions exist.
>
> Reinhold
>
>
Just for refresh:
"Formally, a function f from a set X of input values to a set Y of
possible output values (written as f : X -> Y) is a relation between X
and Y which satisfies:
1. f is total, or entire: for all x in X, there exists a y in Y such
that x f y (x is f-related to y), i.e. for each input value, there is at
least one output value in Y.
2. f is many-to-one, or functional: if x f y and x f z, then y = z.
i.e., many input values can be related to one output value, but one
input value cannot be related to many output values.
A more concise expression of the above definition is the following: a
function from X to Y is a subset f of the cartesian product X × Y, such
that for each x in X, there is a unique y in Y such that the ordered
pair (x, y) is in f."
http://en.wikipedia.org/wiki/Function_%28mathematics%29
Kay
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