On Mon, Oct 12, 2020 at 5:06 AM Wes Turner firstname.lastname@example.org wrote:
SymPy ComplexInfinity, 1/0 < 2/0, *tests* for symbolic results
FWIW, SymPy (a CAS: Computer Algebra System) has Infinity, NegativeInfinity, ComplexInfinity.
Regarding a symbolic result for 1/0:
If 1/0 is infinity (because 0 goes into 1 infinity times), is 2/0 2*inifnity (because 0 goes into 2 2 times more than into 1)
If you try to treat "infinity" as an actual number, you're inevitably going to run into paradoxes. Consider instead: 1/x tends towards +∞ as x tends towards 0 (if x starts out positive), therefore we consider that 1/0 is +∞. By that logic, the limit of 2/0 is the exact same thing. It's still not a perfect system, and division by zero is always going to cause problems, but it's far less paradoxical if you don't try to treat 2/0 as different from 1/0 :)
BTW, you're technically correct, in that 2/0 would be the same as 2 * (whatever 1/0 is), but that's because 2*x tends towards +∞ as x tends towards +∞, meaning that 2*∞ is also ∞.