User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-5150073-20140515153351/@comment-1605058-20140523125650

The fact that we use "first" instead of "zeroth" is just caused by the structure of English language. I must agree that using "zeroth" is technically more correct, though I think we should keep it consistent and all call it "first".