No. It is undefined. That is why they say things like "0/0 is undefined."

Im not convinced or anything buddy, im throwing out some ideas. Take a deep breath. How about the following (which i am open for being wrong):

Division is the operation that yields c from combining a and b ( a/b =c ) such that c*b = a.

So that means if a and b = 0, then every c is a solution, e.g 3*0=0.

An example where division is not defined is when you look at the integers but remove e.g 3, then division is not defined for 12/4 since there is no c.

When you call "division" and "operation" what are the conditions that you are using to apply to the word "operation." That is, what exactly do you view an operation to be?

The standard definition is that division is a binary operation that takes two real number inputs (where the second real number is not allowed to be zero) and outputs a single real number. (Technically, division is a function from RxR* to R.)

So you can say that every c is a solution to the equation you wrote down, but that doesn't help division be an operation.

Okay, so thats the gold standard operator for division you are talking about. And it would have to be modified to allow for 0 in the denominator and it would have to allow output that are both in the form of single elements on R as well as sets on R (since the solution to 0/0 is all the numbers). If i am wording myself correct here.

I guess this is not trivial at all, if you start fooling around with things like that you might affect or influence other parts of math, and maybe start allowing for magic to happen in random equations etc.

Right. You would have to change the output from being real numbers to something like being the real numbers plus some sets, or something like that.

Math has enough weird magic formulas without needing other magic formulas.

The really, really mysterious thing about Mathematicians is that they never riot. Why is that? I would love to be on a campus and hear people shouting and running and exclaiming: The Mathematicians are rioting, they are burning down the physics building and have the University President in chains and are demanding that the number e be declared the Universal arbitrator of all disputes; scientific and political. In addition they are demanding that a chapel be built on campus for the worship of Leonhard Euler. But no, they have to be some sedate boring and monkish group of dunderheads that play fool games with numbers. Wake up and start making some noise you wimps.

Monkish is a good word for it, IMO.

Although I've seen teacups set down in anger over the axiom of choice, I'll have you know.

You would have had a great time during the days of the ancient Greeks. Back then, the Pythagoreans were murderers and thugs, killing in the name of what is true and definitely not eating beans. (Or so you might led to believe if you read the accounts of Hippasus.) And let's not forget Archimedes running down the street naked (though that was really for solving a physics problem, so it might not count).

Those were fun times... I think.

i have seen that vid actually, weird stuff.

I prefer 0v0 because it kinda looks like an owl.

Has anyone done the math to figure out if the reduction in crime we've seen in the US over the past 20-30 years can be solely explained by an aging population? Fewer young punks = lower crime rate. You heard it here first, wheres my check?

There's a complimentary bottle of Victory gin on its way, Foldn.

My theory is television. Give the idiots something to distract them and they're not out raping and stealing as much.

Wow you guys are smart. Thanks for the discussion. Cheers.

Right on! Fight the exponent!

Mathematicians need to emulate Wittgenstein and Popper.

Conclusions first! - then the research and statistics necessary to prove it. Hanging out in the politics forums has really started to soften your already mushy brain Foldn.

I'm sure some save the world foundation will give lots of money to prove what they already know is true. Just do the leg work at finding them and fill out the forms and send it in. Money in the bank.

I hope the teacups and saucers survived such violent treatment.

This is what I'm banking on. But I don't do leg work. I'll sell you the idea for a fair price.

a reason people can learn better than to riot is the fact that authority punishes rioting and violence and can make authoritative statements with backing of claim with such. So learning to non violently participate takes away an opportunity for authority to exploit with appeals to punishment. Moves the appeal to non-violent people, and if authority uses violence it is not the same appeal as these people rioted.

Sets the stage to call for principles of self defense. Assuming a nonviolent person can defend themselves with force or violence and authority uses violence and punishes violence, that principle cannot be applied without being a punishing ethic. There is no rule that ethics must be punishing. So nonviolence becomes the only choice. Avoid giving authority opportunity to punish, and when they do- have a firm appeal that it is unjust. Unjust authority ripe to be outdated. Exposed even.

Maths riot - I wanna riot
Maths riot - a riot of my own
Maths riot - I wanna riot
Maths riot - a riot of my own

Philosophers gotta lot a problems
But they don't mind throwing a brick
Maths people go to school
Where they teach you how to do trig

An' everybody's doing
Just what they're told to
An' nobody wants
To go to jail!

Maths riot - I wanna riot
Maths riot - a riot of my own
Maths riot - I wanna riot
Maths riot - a riot of my own

3 is defined. You gave an example (3 is undefined) that isn't in any number theory, which is an odd thing to do when we are discussing number theory.

Unleaded gasoline and no lead in paint anymore. Fits the data amazingly well.

Also, young men are dumb as ****, so you are also correct.

I can't decide whether that was horrible or horrible.

Thought that was Gladwell's first book. Availability of easy, effective birth control the punchline.

please go bother someone else (its called set theory).