I am reading Chapter 2 of Concrete Mathematics, and have some trouble understanding the rationale behind two identities used for simplification.
1) [1<=j<=k<=n]+[1<=k<=j<=n] = [1<=j,k<=n]+[1<=j=k<=n] 2) [1<=j<k<=n]+[1<=k<j<=n] = [1<=j,k<=n]-[1<=j=k<=n]
Does anyone have any insight on how to prove this, intuition for this or way to think about it. I took some examples of 3X3 matrix and laid out the terms, the relation holds but I don't have an intuition of why it does. Any help is greatly appreciated. Thanks!