sorry, i did not mean that permutation ;) it was just meant to be a visual description of the commutitativity law.
in reply to Re: $a++ allowed by $a-- is not ! why?
in thread $a++ allowed by $a-- is not ! why?
Modern algebra would say that although ++ is one-to-one, it is not onto.
why? it is a mapping from N to N (if i understand you correctly).
-- OTOH (as it is currently defined) is theoretically a permutation over the set of all finite numbers ...
the association is not clear to me. why do you think -- is a permutation? (what is a permutation for you?).
i think we make too much fuss about nothing. perhaps we should continue this by mail?