It just doesn't come up very much. The computers abstract it enough that you rarely need to actually look at notation like that. Unless you're doing some real close to the metal work, which the people who kept their hands raised probably were.

You're mixing up programming with computer science. The former is a task that does not necessarily need any math (e.g. web development), the latter is literally math (e.g. category algebra).

Edit: clarification

It doesn't come up because it is too abstract. About the only languages I can think of that will accept existential statements are theorem provers. My favourite is Isabelle/HOL.

In fact, the notation used by the lecturer is sloppy. Numbers 1..N is not a rigorous domain definition. (Unknown if real or natural.)

I'm not sure I buy your claim that mathematical notation is "close to the metal".