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