I know there is a wealth of information here on SE and also online but I, like many others, have been struggling to get my head around the maths that guide Big O / Big Omega calculations.

I have watched many videos and have found it hard to understand bounds, and particularly how values of c and n_0 are conjured up.

I have written the following mathematical “proof” to find the range for c in an attempt to make sense of it all, and would like some advice on whether what I have written is sound. I am very happy to be critiqued, down-voted, redirected somewhere else, or pegged to a pole and pelted with rotten fruit, I just want to understand this topic better. Many thanks for any advice offered.