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Determine which of the following collections of subsets of R are bases:

a.) C1 = {(n,n+2) C R, n [tex]\in[/tex] Z }

Two things to show are: That every point in X is contained in a basis element, and that every point in the intersection of two basis elements is is contained in another basis element within that intersection.

So, need to show that every integer is contained in C1. I tend to struggle with the mathematical formulation.. although I can see that obviously an integer n will exist in the set on the real line of n, n+2. How would I start?