Week 6

I already used floor and ceiling a number of times before, so the concept was not new to me, just the formal definition. This week, there was only 2 classes and they were both solving example problems, so there's not too much to talk about. In the proof ∀n ∈ N, n^2 + n is even, I am wondering why it is better to factor it to n(n+1), why can't you just try n as an odd and even in n^2 + n? Here I will do it without factoring. It's obviously not a formal proof, just a confident thought process.

Let our even number = 2

Let our odd number = 1

n^2 + n

Odd n = 1^2 + 1 = 2 = Even

n(n+1)

Even n = 4 + 2 = Even

n*n will always produce an even if it's even and odd if it's odd. Adding 2 odd produces even and adding 2 evens produces even also. It's all evens!