Kids are [constantly] judged: bad, not bad; always on trial just like a traffic signal. Contemplating the cosmic conspiracy that’s causing the signal to scream stop as soon as the bus pulls into the lane: why me, why now, everyday, every stop, seriously? etc., I see red or not red–never color. Before I knew, there were some not bad traffic signals-signals not hellbent on turning red at the exact moment my bus is about to enter the black-holes of contemporary life that this traffic has become. (I hope I am not being too harsh.) Basically I produced a structure (bad / not bad) in the domain of traffic signals.
Sure, you did produce a structure in the domain set D of traffic lights with a map f from D to a codomain set C of values (bad, not bad).
Surely, every time I look in the mirror I see myself looking at me.
Sure, the map f: D -> C also produces a structure in the codomain set C of values: not bad is in the minority, bad is more popular :-(
Are we talking about the two uses of maps (Conceptual Mathematics, pp. 81 – 3)?
Each one of the traffic lights in the collection of traffic lights is exactly the way you want them to be: a traffic light.
What, then, happened all of a sudden to these guys leading sedentary lives having resigned to their fate vis-a-vis dogs?
Unbeknownst to the set of traffic signals, as soon as they agreed to be the domain set D of some function f: D -> C, a structure has been imposed on them.
So what? I did the same to the codomain C and it didn’t make a sound, screamed our f: D -> C.
If you let the kids in a domain D run to their moms in a codomain (set of women), then there is no escaping characterizing as not mother, mother, and then split-hairs: mothers with only 1 kid, just 2 kids, exactly 3 kids, and one more kid.
In a world where every woman has a kid (this is a side-effect of bed-time stories exemplifying ART—-stories so creative that nobody who remembers hearing a story can remember hearing it for the first time–I love stories)…
What if I say a world where there are some women with kids and some with no kid? You think the board would be OK with it?
Haves and not-haves is but one structure that we can bring to bear upon a codomain of people P. There are innumerable figures f: M -> P; have / not-have is one of the figures. You have, for example, a dollar and you give it to one of the two guys at the traffic signal and you sketched a figure: one with your dollar, one without. Of course societies have lot more than two under a streetlamp in their collection and still manage to draw the same picture: many with some, some with nothing. It doesn’t have to be that way, it could be an onto function with something for everybody, or that exotic one where everybody either has nothing or exactly one thing. Therefore, broadly speaking, there are only 3 or 4 ways to structure the society!