Is it really impossible to divide by 0?
"What does it mean to divide by zero? In mathematics, this operation is undefined."
So a recent subscriber posted; and the thread was promptly shut down.
I have noticed this tendency in mathematicians to dismiss as "undefined" any question which falls outside their own scrubby patch of competency. Where mathematical philosophy is concerned, "undefined" must always be a confession of intellectual incompetence. There are many questions which were previously "undefined" (notably, the proof that 1+1=2), but which have since been answered.
In the context of the natural number line, the correct equation is:
n/0=Ø
The quotient is a null value indicating that the operation of division fails. Division by 0 is not allowed, and that is a clear enough answer. But in the context of general mathematics, the answer may be infinity, because 0 may be defined as Robinson's h - a value which reconciles the infinitesimal with 0.
So a recent subscriber posted; and the thread was promptly shut down.
I have noticed this tendency in mathematicians to dismiss as "undefined" any question which falls outside their own scrubby patch of competency. Where mathematical philosophy is concerned, "undefined" must always be a confession of intellectual incompetence. There are many questions which were previously "undefined" (notably, the proof that 1+1=2), but which have since been answered.
In the context of the natural number line, the correct equation is:
n/0=Ø
The quotient is a null value indicating that the operation of division fails. Division by 0 is not allowed, and that is a clear enough answer. But in the context of general mathematics, the answer may be infinity, because 0 may be defined as Robinson's h - a value which reconciles the infinitesimal with 0.
Comments (12)
If you divide a pizza by infinity, the pizza is annihilated, presumably, it becomes one with the quantum field.
If you divide a pizza by 1, it is unaltered. Is that right?
If you divide it by 0.5 you get two of them, bizarrely.
If you divide it by the 'opposite' (reciprocal?) of infinity, you get the whole universe, and then some, full up with pizza. Is that right?
So we've gone from absolutely nothing, to the totality of everything. What other options are there that dividing a pizza by 0 will get you? We need something more extreme than either nothing or everything.
Am I talking out of my arse?
EDIT: I've probably made this thread many times worse - delete away.
Its how many half-pizzas you get in one pizza.
You have 5 kids and 10 candies. Each kid gets 2 candies. You have 10 kids, each gets 1 candy. You have 0 kids, how many candies does each ki...
You seem to be under the impression that Robinson's hyperreals define a unique smallest positive infinitesimal. This is false. If h is a positive infinitesimal, then 0 < h/2 < h.
I think you're referring to the limit:
Limit (a/n) = ?
n->0
That's not actually dividing by zero. Here's an article that explains various problems with dividing by zero: https://www.mathsisfun.com/numbers/dividing-by-zero.html
I was referring to such things as the projectively extended real line.