Re:1/0 = 0 (2018)
by BlackFingolfin on Monday December 02, 2024 @05:16AM
(#42294750)
I am a professor for algebra at a research university. I make a point out of teaching my students that `a/b` is NOT the same as multiplying `a` by the multiplicative inverse of `b`.
The standard example is that we have a well-defined and useful notion of division in the ring Z/nZ for n any positive integer even in cases were we "divide" by an element that has no multiplicative inverse. Easy example: take n=8 then you can "divide" 4+nZ by 2+nZ just fine (and in fact turn Z/nZ into a Euclidean ring), even though 2+nZ is not a unit, i.e. admits no multiplicative inverse.
Reusing symbols in a different context is pretty common; taking a symbol that is already broadly used in a specific way (in this case, that `a/b` is defined for elements in a field as multiplying `a` by the multiplicative inverse of `b`) is poor form and, frankly, a disingenuous argument.