Question regarding Monoalphabetic Phi Test
Where , some text, n= length of text , size of the alphabet, and the frequency of a letter from the alphabet within the text.
Finding the equalities was relatively easy; they exist when the size of the alphabet, , is equal to one.Where I'm having trouble is proving the inequalities. I can pretty much see that, due to being a sum of frequencies, it'll always be less than one, but should I be proving this with induction? And further, I can't really see how to prove that . Again, I can see how it works, and I've done it with a few examples, but I'm not too sure how to translate that into a rigorous proof.