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Abstract Algebra 79: The ring of all functions from the reals to the reals
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Abstract Algebra 79: The ring of all functions from the reals to the reals
Abstract: We discuss why the set of all functions from the real numbers to the real numbers has the structure of a ring. Indeed, the operations are pointwise addition and pointwise multiplication. Under addition, these functions form an abelian group. And the multiplication is associative (here also commutative) and distributes over addition.
This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University:
Abstract: We discuss why the set of all functions from the real numbers to the real numbers has the structure of a ring. Indeed, the operations are pointwise addition and pointwise multiplication. Under addition, these functions form an abelian group. And the multiplication is associative (here also commutative) and distributes over addition.
This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University:
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