Useful Math: 1. What is a Set?

A set is any collection of things. In math this is usually a collection of numbers. But in the real world this can be a collection of clothing items, car companies, fabrics or anything you can think of.

The main thing to remember is that sets are made of things in common with other things. The set of odd numbers would be 1,3,5,7,9, etc. The set of clothing items would include shoes, t-shirts, jackets, pants, etc.

You can even make a set of (seemingly) totally different things as long as you say they are in the same set. An example would be the set of white chairs with yellow spots and slow runners named Stacy. The only commonalities they seem to have is the fact that they are named as part of that set. However, since the definition of that set contains them, they do have something in common (namely, the definition of the set).

Sets are usually symbolized with these squiggly parentheses called “braces” shown here:

{}

They are also usually given a name symbolized with a single, capitalized letter.

The set of car companies would thus be shown like this:

The set of car companies “C” is {Toyota, Ford, Honda, …}.

The ellipses would indicate the “etc.”

Sets are used a lot in analytic philosophy. This means they are also used a lot in logic, even if they aren’t explicitly symbolized or stated.

Sets, for example, are used a lot in categorical logic. Whenever you categorize a collection of things into a set, you are making a categorical statement. “All brown things have brown in common.” “Some t-shirts have the color red in common.”

This means that sets are really “abstractions” of things. That is to say that we take something a collection of things have in common and “abstract” it by giving them a category title. “Shoes, t-shirts, jackets, pants, etc.” are abstracted into the set called “clothing items.”

The tasks for today are to 1) meditate on what things we intuitively categorize into “sets” in our minds and 2) try to live the next few days with an awareness of when we subconsciously group things into sets.

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