Help with sets

[Steve Howell]

On Oct 13, 4:27 pm, Lawrence D'Oliveiro <l... at geek-
central.gen.new_zealand> wrote:
> In message
> <57a322df-8e42-4da5-af96-0c21c5733... at b14g2000pro.googlegroups.com>, Steve
>
> Howell wrote:
> > Lawrence, I was actually talking about symmetry, not orthogonality.
>
> So what’s the difference?

I don't think there's a big difference between the two--you snipped
away my comment about them often going hand in hand, so I will repeat
it here that they do often go hand in hand.

I guess a lot depends on how you define "symmetry."  Is your
definition of "symmetry" equivalent to your definition of
"orthogonality"?

I don't have a precise definition of "symmetry" myself, I will admit.
Perhaps for lack of a better word, I throw around the term "symmetry"
for situations where analogous constructs get used in slightly
different contexts.  The example in this discussion is the "in"
keyword.  You can use "in" for strings, sets, lists, and dictionaries,
which in and of itself is an example of "symmetry" in my mind.
Another example is the relationship of the "+" operator to the "*"
operator.  With numbers "*" connotes repeated use of "+", as it does
with strings, even though the underlying operations for "+" are not
exactly equivalent.  String star-ification is repeated concatenation,
whereas integer star-ification is repeated addition, but since
concatenation and addition are both represented by "+", it creates
some sort of symmetry to have "*" as the string-concatenation-
repetition operator, even if it is not something folks commonly
encounter outside of programming languages.