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Good Math by Mark C. Chu-Carroll

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20Group Theory: Finding Symmetries with Sets

Every day, most of us get up in the morning, go into the bathroom, and brush our teeth in front of a mirror. When we do that, we’re confronted with a profound mathematical concept that we rarely think about: symmetry.

Mirror reflection is the kind of symmetry that’s most familiar to us because we experience it every day. There are many other kinds of symmetry: symmetry is a very general concept that comes up everywhere from math to art to music to physics. By understanding the mathematical meaning of symmetry, we can see how all of the different kinds of symmetries are all really different expressions of the same fundamental concept.

To understand what symmetry really is, we’ll use the LEGO-like ...

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