I took it more like the way you specify certain jQuery operations such as:

    $('.card').hide();

to mean "hide all cards", or

    $('.card.green').show();

to mean "show all green cards". It's really comfortable to think about operating on the set like this and not having to worry about looping on the individual items.

In fact thinking of it as a set frees computing to do things concurrently invisibly.

A lot of other comments here say "ah, but that's just JS iteration still"... but there's really nothing to prevent it being the equivalent of a Go routine... no order implied, no iteration implied, but all the things in the set will have the functions hide() or show() called.

I am not sure that would count as working on the set. It looks like iteration.

From the article:

a) 1___ 2___ 3___ 4___ 5___ 6___ 7___ 8___ 9___

Thinks of them as a set or subsets of entities and operates on those, or specifies them with plurals. Example: Buy all of the books that are red.

b) 1___ 2___ 3___ 4___ 5___ 6___ 7___ 8___ 9___

Uses iteration (i.e. loop) to operate them explicitly. Example: For each book, if it is red, buy it.

In your case it looks like you are operating on each item and not on the set.

It sounds very like array programming, eg APL and it's derivatives

That's just Array.forEach in JS. Or in Scala:

  (1 to 5) foreach { _ =>
    println("look, a line!")
  }

That's really nothing to do with Sets.

Logically it can be expressed as operating on the set {1, 2, 3, 4, 5} - I think that's the point: one can perceive it differently, either as a set operation or as a loop/iteration.

  module Numeric
    def times(&b)
      (1..self).each(&b)
    end
  end

It's really no different than the Scala you'd write for the same thing:

  implicit class LongHelpers(l: Long) {
    def times(f: => Any) = (1L to l) foreach f
  }

  10 times println("here's a line!")

To interpret that as a Set operation would make the definition of a Set operation so broad as to be useless IMO.

sets aren't ordered

The set of ordered sets is a subset of the set of sets. Totally ordered sets, which I think are synonymous with chains(?), are still sets.

But yes, I was talking loosely: my point was to differentiate between a mental model of iterating over a sequence (or ordered set) and applying a set-like transformation. My mental picture was of a field formed by a matrix operation on a limited space as being composed of the summation of a series of vector transformations; my maths language doesn't really allow me to properly describe it however. Loosely: you can break down a [subset of] 3D transformation[s] of a surface in to a series of 2D transformations performed iteratively, or you can apply a 3D transformation; they're different mental images of acquiring the same result.