In what ways are students in grades 7-12 exposed to the mathematical concept of "inverse?" The few I've thought of are inverse operations and finding the inverse of a function. Any others?
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1Operation : "fasten shoes" vs "loose shoes". – Mauro ALLEGRANZA Oct 03 '19 at 15:26
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@MauroALLEGRANZA To build on your idea, the "shoes and socks" theorem states that if you want to take off your socks, you first have to take off your shoes. Hence $(gh)^{-1} = h^{-1}g^{-1}$ except for certain commutative operations. – David Kraemer Oct 03 '19 at 15:35
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2Not except for certain commutative operations. Then the formula still holds. For more such examples see here. – Dietrich Burde Oct 03 '19 at 15:36
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I was imprecise. I meant "which cannot be reduced except for certain commutative operations". – David Kraemer Oct 03 '19 at 15:41
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1Inversion w.r.t. a pole in geometry is another. – Bernard Oct 03 '19 at 15:59