I came across following two statements on independent set wikipedia page:
A set is independent if and only if its complement is a vertex cover. Therefore, the sum of the size of the largest independent set $α(G)$, and the size of a minimum vertex cover $β(G)$, is equal to the number of vertices in the graph.
I get the first sentence. But I didnt get the second sentence. Particularly I didnt get why it uses words "largest" and "minimum". If (as stated in first sentence) independent set and vertex cover are complement of each other, then sum of sizes of any independent set and its complementing vertex cover should result in total number of vertices in the graph. So is it a mistake on wikipedia page or am I missing something?
You both are right, but in Wikipedia is considered only a particular pair (the largest independent set, a minimum vertex cover) which corresponds to values $\alpha(G)$ and $\beta(G)$, whereas you consider a general case, for which this correspondence may not hold.