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You need to read it as: "Set theory is a language through which all of math can be described." Think of this example: Set A is the set of all maximas and
by __rito__ 3y ago
You need to read it as: "Set theory is a language through which all of math can be described."
Think of this example:
Set A is the set of all maximas and minimas of the polynomial function f(x).
Now, to populate the set you'll need to do Calculus. But it is described in the language of set theory.
There are many more examples that can be given:
Set X is a set of all non-prime integers between 2,000,000,000 and 3,000,000,000. (Number theory)
Set Y is a set of all the eigenvectors of the transformation matrix A. (Linear Algebra)
And so on.
This is just one of many ways set theory describe math. In my understanding, it makes human-to-human communique on Math much more efficient, but it is not limited to that.
If there is a new field where you can show that you can satisfy tenets of set theory, then rules of set theory applies to the new field as well.
This pattern is most profound in Linear Algebra. You use it in Deep Learning, Geometry, Equations, Non-Linear Dynamics, Quantum Computation/Physics, etc.