…And You Are Also a Set

Strolling through some high school hallways, you can see many cases of math in action. You have the jocks clustered by the senior wall, the musicians singing and playing some tunes in the band wing, the science olympians bent over their textbooks and calculators in the library. All these groups, seemingly barred from each other by the unspoken laws of high school, are sets.

Mathematically, a set is a collection of objects called members, or elements. Set “Jocks” consists of that guy tossing a football in the corner, those two girls in the corner with lacrosse sticks in hand squealing about the win yesterday, and others. Set “Musicians” consists of the piano prodigy composing a piece on the spot, to the girl singing vibrato on the top of her lungs.

However, we all are a coalescence of crooks and crannies, little perks and pet-peeves, love and hate; we are fragile bodies filled with thoughts, epiphanies, ideas: we are collections of elements that make us us.

Looking at the cliche clusters of high school, it’s safe to say that we are all elements of a set, all members of a collection no matter how much we insist that we are independent from anyone else. But aside from these facts is the cool things you can do with set theory. For example, a union of sets of two sets A and B is the set of elements which are in A, in B, or in both A and B. And thinking in terms of high school, set Jocks in union with set Science Olympians would breed a set with both jocks and science olympians… But let’s be realistic here; in the unwritten laws of high school, this set is unheard of yet mathematically, it’s sound.

Realistically:

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Mathematically:

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However, I’m interested in how sets pertain to ourselves, how we are the sets themselves. Because as I see it, I am a set; I am made of of elements and characteristics that make me me, from my curly hair to my love for strawberries and nutella. On the other hand, my friend Odeya might be a set consisting of the elements “passion for journalism,” “love for stepping outside the comfort zone,” and others. However, we all are a coalescence of crooks and crannies, little perks and pet-peeves, love and hate; we are fragile bodies filled with thoughts, epiphanies, ideas: we are collections of elements that make us us. Further, we are all sets that are subsets of bigger sets; I am a subset of Strong Young Women, while you might be a subset of Leaders.

There’s something in set theory called Russell’s Paradox: Let Z be the collection of all sets which do not contain themselves as members. Does Z belong to itself or not? This is the same thing as the Barber Paradox: “In a small town, where every man is clean-shaven, there is a barber. This barber shaves all men who do not shave themselves and only men who do not shave themselves. Who, then, shaves the barber?” The barber cannot shave himself, because he does not shave the men who shave themselves. At the same time, if someone else shaved him, then he would not be shaving himself, meaning he should be shaving himself, but then he can’t because he does no shave the men… ah, the frustration. but this idea was so perplexing to mathematicians since it was essentially a
“flaw” in set theory, which led to the idea, do sets belong to themselves? Some can, but not all the time. 

The idea of “belonging” applies outside of math, however. If I asked you, “Do you belong to yourself? Does your set belong to you?” you would most likely scoff and say, “Yes, of course!” But think about that statement. Are you ever continuously forced by your parents, or peer pressured by your friends to do something? In these cases, you don’t really belong to yourself; you belong to whoever is forcing you to do something. It might be confusing to think about, but I truly think there are so many people out there who don’t belong to themselves, who are not themselves; they don’t belong to their sets.

Before you go, think about this: What’s your set? What are you a subset of? Which elements, characteristics make you, you? And, do you belong to yourself, your own set?

 

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One thought on “…And You Are Also a Set

  1. Here is a quote from Groucho Mark about belonging to certain sets: “Please accept my resignation. I don’t care to belong to any club that will have me as a member”.

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