Ok Im a bit new and my mathematical proof knowledge and practice is novice will, its not much as I'm only a few weeks into an algorithm and design paper and am a little learning challenged. I am trying to wrap my head around a several lab question questions and I'm hoping that if someone can help me with this I will build a little momentum and be able to answer the harder ones under my own steam.
I have a definition: Let f, g be functions. If there exist c, n0 > 0 such that,for all n > n0, f(n) ≤ c · g(n), then f(n) is O(g(n))
Have to prove this using the definition.
For every function f : N→N, f(n) is O(f(n)).
Now firstly I'm confused bu the face that g(n) isnt in this question but it is in the harder ones so I know it isnt a typo. I'm thinking that it is the same function so shouldn't it be big theta? I am very confused. Also how to present this as a proof is also quite mysterious to me. Can I do this as a direct proof?
Most appreciate any help.