A BRAND NEW Arithmetic Operation! | Intro to Group Theory for ALL
In this video, I define an "arithmetic operation"
a*b = a + b + ab
for real numbers a and b. The arithmetic operation satisfies all the usual laws that ordinary addition and multiplication satisfy, namely, associativity, existence of an identity and existence of an inverse for each number ≠ -1, which makes the set of real numbers (except -1) an abelian group with respect to the operation *. I explain in detail what this means in a very accessible way (to anyone who has at least some familiarity with algebra at the high school level), and this video also furnishes an introduction to group theory and abstract mathematics for EVERYONE! 🥳 🎉 🎊
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