A binary operation takes two things as an input (called operands) and produces another thing as a final result (“Binary operation,” Wikipedia).
If a you perform a binary operation on a set[1], then (usually) both operands and the final product are in that same set (ibid.). To elaborate, the “two domains and the codomain [of the operation] are [usually] the same [as the set being operated on]. Examples include the familiar arithmetic operations of addition, subtraction, multiplication. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication and conjugation in groups.” (ibid.)
All quotes were retrieved 10/8/2020.
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[1] See “What is the Gist of a “Set” (Mathematics)?“
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
