Is it really impossible to divide by 0?

alan1000

"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.

bert1

I'm just an idiot who knows nothing about maths, but I'm just wondering what dividing by 0 might mean in terms of pizzas.

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.

Apustimelogist

If you divide it by 0.5 you get two of them, bizarrely — bert1

Its how many half-pizzas you get in one pizza.

flannel jesus

↪Apustimelogist

or how many pizzas you can buy, if they cost 50 cents each and you have a dollar.

tim wood

"What does it mean to divide by zero? In mathematics, this operation is undefined." — alan1000

Or maybe in this, as with many, contexts "undefined" is simply well-understood shorthand meaning don't do it for lots of good reasons.

Michael

There are some number systems that define division by zero as ${a\over0} = \infty$ .

Lionino

What other options are there that dividing a pizza by 0 will get you? — bert1

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...

DifferentiatingEgg

It would be like trying to cut you with air, and without any force behind the air.

Johnnie

https://en.wikipedia.org/wiki/Projectively_extended_real_line

fishfry

0 may be defined as Robinson's h — alan1000

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.

Relativist

There are some number systems that define division by zero as a/0=∞. — Michael

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

Michael

↪Relativist

I was referring to such things as the projectively extended real line.

Relativist

↪Michael

Very cool! I took only one class in Real Analysis (decades ago), and this is an interesting extension that I was unware of. Gracias!

Is it really impossible to divide by 0?

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