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Look at it this way... Standard definition of division function, d: d(x, y) = x * y⁻, for all x and y EXCEPT 0 Author's modified, piecewise (https://en.wikip
by a_wild_dandan 8y ago
Look at it this way...
Standard definition of division function, d:
d(x, y) = x * y⁻, for all x and y EXCEPT 0
Author's modified, piecewise (https://en.wikipedia.org/wiki/Piecewise https://en.wikipedia.org/wiki/Piecewise) definition:
d(x, y) = x * y⁻, for all x and y EXCEPT 0
d(x, y) = 0, for y = 0
He's just adding 0 to the domain of d(x, y) to extend the definition, and deliberately not using xy⁻ for that particular element of the domain. No inverse needed.
- sclv 8y agoI know what he's doing. The problem is when you make it a different function (even by just extending it) then you change its equational properties. So equational properties that held over the whole domain of the function no longer hold over the extended domain. This is repaired by modifying the equational properties. But the modified equational properties mean that you now have a different system than before. So the whole thing is just playing around with words.
- deleted 8y ago[deleted]
- mdpopescu 8y ago> So the whole thing is just playing around with words. Er... that's what mathematics is. It's a word game - we build systems from arbitrary rules and then explore the results. Look through https://www.mathgoodies.com/articles/numbers https://www.mathgoodies.com/articles/numbers for a bunch of uncommonly-defined numbers.