I am a high school student of Mathematics. I have been working on this piece-wise function, trying to understand its properties:-
[N is the set of all natural numbers, W is the set of all whole numbers. The mod function gives the remainder when n is divided by 2]
I thought of finding a single function that has the same value as that of this piece-wise function in its domain, and trying to evaluate the properties of the new function. Firstly, is that a good idea? Or, is there another way out?
I want to find properties of the function so that I can subject it to further algebraic treatment. Also, please guide me to systematically analyze the function so that I can derive fruitful results using the same. Thank you for any help!