How is even and odd related to + and - because 2 odd functions or 2 even functions (and permutation groups too) are multiplied together to give an even result. If they are different like odd even then we get odd exactly like how scalars with the same sign gives a positive and numbers with opposite signs gives a negative. If even is analogous to positive and odd is analogous to negative then what would be analogous to neither even nor odd (0)… In fact can the concept of even and odd somewhat in a clever way be extended to reals such as 1.253?
A lot of cool thoughts to explore possible extensions. Would like some help with this because I am (relatively speaking) a newbie compared to graduates.
Functions behave differently under multiplication and composition.
When you multiply two even functions the result is an even function
When you multiply two odd functions the result is an even function
When you multiply an odd and an even function the result is an odd function.
When you compose two even functions the result is an even function.
When you compose two odd functions the result is an odd function.
When you compose an odd and an even function the result is an even function.
You can find similarities between functions behavior with addition and muliplication of integers