What is an umbiff?

The word umbiff is a new age noun, seeking to fill a hole in the English vocabulary. Have you ever tried to explain the relationship between two items that nest inside of one another?

Jimmy, I'm confused. How is a power series different than a geometric series?
Billy, we've gone over this so many times. How many times do I have to explain this to you?
Come on, you have to lock in for this exam.
I know, Jimmy. Can you just explain it one more time?
Every geometric series is a power series but not every power series is a geometric series. It's like how every square is a rectangle but not every rectangle is a square. You know, the square-rectangle thing.
Oh yeah, I remember now.
I wish there was a simpler way to describe that relationship...
You know what, I think I've heard of something like that before. I think it's called an umbiff!

Definition

Umbiff

/ˈʌm.bɪf/

noun

An umbiff is a casual phrase to represent a relationship between two sets and in which every element of is also an element of , and contains at least one element not in .

Example: "Since every square is a rectangle but not every rectangle is a square, the pair (square, rectangle) is an umbiff."

Etymology

The word umbiff has arisen within the past century. It is rumored that a group of four college students were on spring break in Florida. They were walking over a rickety bridge, high up in the air, with metal grates as flooring. One said, "There should be a word for that square-rectangle thing."

The other replied, "How about umbiff?"

"Well, how do you spell it?"

"U-M-B-I-F-F. Like an homage to if and only if."

They made it over the bridge safely and have been using the word umbiff ever since.

Usage

Although the word umbiff shares a strikingly similar definition to a proper subset, the notions are indeed different in their connotations. Umbiff is more casual. One can simply say, "every procedure is a subroutine but not every subroutine is a procedure," while the other replies, "Umbiff!" and they both go on with their day. Notice how there is no need to understand what sets are, what A and B are, what their elements are, etc. Umbiff expresses their relationship on a lower level.

We would also like to note that umbiff is not a verb nor is it an adjective. It is simply an umbiff and it requires exactly 2 items. cannot umbiff , and is not an umbiff if not for . We only say that and are umbiffs together. Together they make one umbiff.

Properties

Transitivity

If and are umbiffs and and are umbiffs, then and are umbiffs. If every square is a rectangle but not every rectangle is a square and every rectangle is a quadrilateral but not every quadrilateral is a rectangle, then we can say that every square is a quadrilateral but not every quadrilateral is a square.