Division by zero isn't possible

Division by zero isn't possible

or is it really just an infinite result...
/thread

t. Nietzsche

...

> X/0
> divide X by nothing
> X/0 = X
solved it :^)

epik

It is if you define it

If you define it to be possible you get contradictions like 1=2. Just like defining 1 to be prime contradicts the fundamental theorem of arithmetic. I'm not asserting that any position on either of these topics is correct, I'm only illustrating a point.

You can't just divide something into 0 parts. Something/Nothing = Impossibru.

I am afraid it is possible since nothing doesn't exist. Therefore 0 exists and can be element of division.

AYY LMAO

>defining 1 to be prime contradicts the fundamental theorem of arithmetic

>l'hôspital rule

>implying zero has a multiplicative inverse
What number system do you use OP?

> what is wheel theory

Dividing by zero will give you infinity. But it is undefined because it allows you to get answers like 1=2.

Fucking summerfags actually think dividing by zero means putting nothing into something.

6 / 2:
6 - 2 = 4 [1]
4 - 2 = 2 [2]
2 - 2 = 0 [3]
There 6 / 2 = 3 because it takes 3 'steps' to get to 0 by subtracting 2 each time.

6 / 0:
6 - 0 = 6 [1]
6 - 0 = 6 [2]
6 - 0 = 6 [3]
...ad infinitum

By this logic, 4 / 0 also = infinity. Therefore we can 6 = 4. This is why division by 0 is undefined.

Division is just how many times you can subtract.

Isn't it because:

a/b = c

c x b = a

I'll do whatever I want.

>Ln(0) doesnt exist

>he used an accented o for the english spelling of a french word

Another possible interpretation on division is multiplication by the multiplicative inverse of the number you want to "divide by".
[eqn]a / b \quad \equiv \quad a \cdot \frac{1}{b}[/eqn]

> muh minus Inf

Easy. Compute everything on the Riemann sphere.

Because fuck normed division algebras.

Riemann """"""sphere""""""

yay 0=1

Sky's blue dude.

It's a sphere in every sense of the word.

No, because 1 / b is a division.

You can't define anything in terms of itself

What's the radius of the sphere?

> That's why limits were invented, dumbass. Limits makes it possible to do operations that were impossible before and that's why we consider Leibniz to be a genius.

Expand the real numbers so that there exists the number o such that

1/0 = o

You can multiply it.

n*o = n*(1/0) = no

You can add to it.

n + o = n/1 + 1/0 = (0 + 1)/0 = o

Now to show that the real numbers with o still form a group.

*0 is still the additive neutral element

0 + o = 0/1 + 1/0 = (0 + 1)/0 = o

* -o exists and is the additive inverse of o

o - o = 1/0 - 1/0 = (0 + 0)/(0) = 0*(1/0) = 0o = 0

* addition is associative even with o

(a+b) + o = (a+b)/1 + 1/0 = (0 + 1)/0 = o
a+(b+o) =
b+o = b/1 + 1/0 = (0 + 1)/0 = o
so
a+(b+o) = a+o = o (the computation has been done many times now)

therefore (a+b)+o = a+(b+o) and therefore addition is still associative.

So this new set with addition still forms a group.

To complete the field structure:

* addition is commutative.

n + o = o = o + n (the computation is trivial)

* multiplication is associative

a*(b*o) = abo = ab/0
(a*b)*o = abo = ab/0

so they are the same.

*multiplication is still distributive with respect to the sum

o(a+b) = (a+b)/0 = a/0 + b/0 = ao + bo

Therefore the real numbers with o works pretty okay.

We could also try to implement an order that fits.

o > any other real number (not including o itself)
-o < any other real number (not including -o itself)

a + o > b + o if and only if a > b
a - o > b - o if and only if a > b

a - o < a + o is always true

etc.

Correct frogposter.

Is this extended reals?

It does extend the reals but I just made it up, it is not some established system people actually use.

But then by that logic 0/0=0.

0/0 = 0
0/0 + x = 0 + x
0/0 + x/1 = x
(0 + 0)/0 = x
x = 0/0

So by that logic, 0/0 = any real number.

more like t. engineer fag who took calc 1

Riddle me this, shitheel:

If the square root of -1 is somehow also a valid number, why not 1/0?

It makes sense because it would be like the complement to imaginary numbers, when raised to negative powers they would become real again

>not knowing the difference between impossible and undefined

Senpai! don't forget about me desu
~ln(0)

omg you're a genius
why isn't 0^ln(0)/0 a valid number either wtf?

What are you implying?

one within zero