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Demolishun1554763dI always felt like anything divided by zero was infinite. Like how many zeros can you fit in a number? I am also fascinated that this is a whole dimension unto itself where it never stops. Even 0/0 seems to go on forever as it never fills zero. Or is it 1 because they are equivalent? You could add infinite zeros to still have 0.
GeorgeBool252663dDidn't understand shit, but here's what my caveman brains are thinking:
 Infinity big? This too big, ret symbolic constant.
 Infinity smol? This too smol, ret symbolic constant.
 Nothing? This nothing, ret zero.
So infinity>epsilon>zero>-epsilon>-infinity or some shit like that must hold true for the universe not to split apart. BUT infinity itself is made-up, because I can keep counting up I just get tired after FF.
Now if I split whole times infinity I get infinite times the smallest number, and if I split whole times smalles number I get infinity. Split times nothing? First off, why. Second, how. Where do we split? There is nothing to split times by.
But my "understanding" of math is between quotes. That is both literal and figurative. I know some of the useful stuff and then there's the steamy midnight action. Ugh, disgusting. Yall motherfuckers need Jesus.
iiii715163dBecause zero breaks inversion in division.
If 6/0=0 then 0*0=6, which is false. So either multiplication by zero or division by zero would be undefined. And while multiplication by zero makes sense in common arithmetic, division does not.
You can, of course, use limit to determine the answer but you'll get infinity.
WizardOfAus463d0/a = 0
a/a = 1
a/0 = infinity
Now set a = 0 and we have 0 = 1 = infinity
That's just stupid, so /0 is "indeterminate" which is code for arithmetic has a bug so don't do this.
The real question is how you made it out of high school without learning this.
theabbie828263dWe take 1/0 as infinity as that is what anyone would expect 1/x to be as x almost becomes 0, though it would also become -infinity is we approach from negative side, It is undefined at precisely 0, but since it approaches infinity, we say it's the highest number you can possibly imagine.
There is no reason for 1/0 to be 0, it does not approach 0 at all.
As others said It's undefined. That is because 0 isn't really a normal number. I read a book on this a long time ago where it was explained, that 0 wasn't defined at all when math just started out. You could own 1 chicken, 5 chicken, but if you couldn't own none chicken. It's unintuitive to say "Hey, I have 0 chickens, wanna trade?" So initially the concept of an empty quantity wasn't even defined. Then once we figured out that It's useful to have a name for an empty quantity we started putting it into math and it turned out it doesn't work, which is why we had to define it and Its special rules and behaviours rather then just add it as another number. So now you just have to accept that that is how it is, because it just doesn't work like a traditional number.
For example for Multiplication, we have the identity property that states that 1 * a = a; where a can be any real number
Indeed if you have 1 times 6 chicken, you have 6 chicken and the same works for 0... Ok cool... But this rule also states, that the inverse must exist
(1/a)*a = 1
Well ok... This works for 6... It you have a one sixth of a chicken six times, you have 1 whole Chicken... Kinda weird to think about, but its intuitively true!
Lets try that for 0 now!
If you have 1 nothing-th or a chicken no times you have 1 whole Chick... Wait a second... Where did this chicken come from...
Even if you think about it in terms of a split it breaks the rules... If you split a chicken 0 times (1/a).. and then you have this unsplit Chicken 0 times (*0) you should still have an unsplit chicken... But you just said you have it 0 times... So... wait What?!
Ok ok.. so different approach! Lets say instead that I split this chicken into 0 sized chunks! 1/0 == Infinity right?! Well ok, you have an Infinite amount of non-chicken chunks that put together a one whole chicken somehow, but that doesn't solve the problem of having it 0 times... But you should still have one chicken if you follow the axioms of Multiplication.. (this shows you why divison by 0 is undefined. It may or may not be intuitive based on your situation entirely)
So what gives? Well simply put, 0 is a nonsense quantity, and you have to work around it yourself, because It's useful to have, but at the same time it doesn't work at all... So what do you do as a mathenatician? You definy it... You say "this will be a number, It's even an integer, but here is a set of rules of how to work with it that actually reflect the real world"
Avyy78462dContext: The identity element(e) is an element such that for any element in the domain set, `a*e = e*a = a`
The inverse element(i) of an element is defined such that `a*i = i*a = e`
Each non-zero element has its own unique inverse(in the set R)
Not going into more theory, just convincing you by contradiction here:
Let `0/0 = k`. Then `0 = 0*k`.
Now what do you think should be the value of k here? Zero? Infinity? Something in-between?
It can be anything, all numbers on the number line satisfy this. We say, this value is "indeterminate", it just can not be defined.
Bonus: Contrary to popular belief, 0*inf is also undefined. It is not zero, not one, not infinity; it is nothing.
rov3rand0m61862d@iiii if 0*0 was 6,
That would be true for any number then 0*0 would be anything
This would basically break everything in math, right?
This is so fascinating. I think the original question in the post is very interesting. Because instead of taking the math rule as granted, it pushes logic to its limits.
natesymer21262dHow many times does nothing go into something? An infinite number of times. Geez, this is calc 1 shit you should have learned in college. If you look at the fn 1/x, you'll see that there's a vert asymptote at x=0....
Oh shit, I figured out what 0/0 is! It is a cat! But I cannot tell if it is alive or dead...
And, btw, limits can show why 0*infinity is undefined.
0 is lim(1/n)
Infinity is lim(m)
Then 0*infinity is lim(m/n) and here's the catch:
- if n rises faster than m, then the result is 0
- if n rises slower than m, then the answer is infinity
- if they rise equally fast then the answer is 1
if you start doing this shit you break math and nothing makes sense anymore.
you can approach the division by zero with limit (tends towards infinity), but the actual value does not exist.
the problem you proposed is a little basic, a more interesting approach would be 0/0 = 1
Wisecrack589062dWell apparently the question is retarded.
At least a billion google searchers will now find their way to devrant.
Unfortunately they too, like myself, will be retarded.
Great answers though everyone.
I got an A on the assignment.
(Im kidding, im kidding! dont throw anything at me!)
Wisecrack589061d"(1/a)*a == 1
Well ok... This works for 6... It you have a one sixth of a chicken six times, you have 1 whole Chicken... Kinda weird to think about, but its intuitively true!"
Treat it as a mathematical object for a second.
And forgive my ignorance for moment, what I mean is this.
If (1/a)*a == 1
suppose this object carries around its identity.
Think about it
(1/a)*a doesnt really equal 1 does it?
We're actually assuming a term here. We're not showing it...
(1/a)*a == 1*1
That second term is what we're leaving off there. Its the multiplicative identity yeah?
Well in the case of a=0, its not
(1/a)*a == NaN
It would be a special case:
(1/a)*a == 1*0
"a/0 == infinity"
No, I'm explicitly arguing that just as 0/n == 0, n/0 == 0 remainder n.
"How many times does nothing go into something? An infinite number of times. "
Whats makes more sense?
That *nothing* can be divided into something infinite times, or that nothing divides exactly *zero* times into *anything*?
Last I checked zero is still zero, no matter how many times you divide it.
I actually emailed a bunch of people, and got a response from an undergrad at michigan u. he wrote out a sketch of a proof of this and accompanying code even. Idk if you want to check his work its here: