Okey, im fairly sure this is simple but i've not done maths in ages and we have horrendous maths lecturers and tutorial people who's reply when our whole table couldn't do it was 'Guys, it's easy, why dont you get it?'

Now im not asking for the answer, just some help if that's ok .

The question is:

$\displaystyle

f(x) = \lceil\frac{x}{4}\rceil - \lfloor \frac{x}{4} + \frac{1}{4} \rfloor

$

Now the part in brackets is meant to be floored. And the part not in brackets is mean to be ceiling.

Question:

Prove:

a.) If n is an integer then f( x + 4n) = f(x)

b.) If 0 < x < 3 then f(x) = 1 and if 3 < x < 4 then f (x) = 0

Ermmm...we've been taught...very briefly proof by induction so i'm assuming this needs to be used? But i have no idea how to apply proof by induction to this...if you add 1 to the f(x + 4n) to get f ( x + 4n + 1) you're just going to get f(x + 1) as the final result and that just seems pointless to me an unproved :S.

Any help would be appriciated!!! Even if you could just link me to something handy =). Thankyou so much x