OK, what a day of goodness from remote corners

I most of all appreciate Jeff Moden’s top to bottom explanation of the query, but all posts deepened the understanding of many concepts and creativity that goes into clever SQL.

I get the asci and non asci standard for cross apply notation (which I didn’t before, particularly because I was tripped up with the ‘x’ thinking it was a multiplication symbol instead of an alias), the UNION ALL replacing the VALUES syntax (whose x n I didn’t and still don’t understand but don't have to), replacing derived queries with CTEs, CTE syntax/structure, explaining 1 as placeholder so you have something to assign to row_numbers, harnessing Row_Number to get rows numbered by using the ORDER BY NULLs trick, appreciate the performance observations...but….why the row numbers have to start as ZERO still eludes me…..even if Lowell gave an explanation that smacked of something that I should get, and even though ‘ it is simple math’. I thought I knew simple math. I now see how it works (ie. I tested it with and without zero, at least I can see the purpose), but not why.

The - 1 is more about logic than math....and I don't expect you to help me there actually.

So, you people are pretty wonderful. Thanks.