1/x as x good to 0 from the positive side is infinity, but that's just a one sided limit
x/0 it's undefined for all x because it's division by 0 (which is really multiplication by the multiplicative inverse of 0, which I'm pretty sure can only exist in fields that only contain one element, so 0=1)
undefined means that it wasn't given a definition. 0/0 isn't usually given a definition, so it is undefined. The reason why it's undefined is because there is no good way to define it, since it's an indeterminate form.
It's indeterminate, which essentially means we don't have enough information to solve the problem.
This isn’t a perfect way to explain it, but try this on for size: Broadly speaking, we measure speed by seeing how far an object moves in a certain amount of time. If the car moves three meters in one second, it is moving at three meters per second - three meters divided by one second. If it moves three meters in half a second, then we have three meters divided by half a second, giving us six meters per second. Really simple, right?
Let's stop time.
Now, let's look at all these cars over here. They all move... zero meters... in zero seconds. How fast are they going? Are they stopped? Are they moving backwards? We have no way to know, because we're not actually measuring anything meaningful at this point. 0/0 is indeterminate.
And, incidentally, x/0 (where X is not zero) is undefined because if you stop time, and one of the cars is still moving, then that doesn't make any sense. Time is stopped, so it shouldn't move at all. It's breaking the rules. Nothing makes sense anymore. You can no longer rely on this system of measurement *at all* - you can actually prove that 1=0 if you're allowed to divide by zero. So we don't allow that - we say that it's undefined, which means it's against the rules of math.
Thing is though if it could be 1, it could also be 5, because 0 * 5 = 0, so divide both sides by 0, you get 5 = 0/0.
So literally any number could be "equal" to 0/0 if we allowed 1.
It’s a good comic that would’ve been better if they didn’t make that little error. I suppose it’s generating discussion, but it makes me wonder if the author didn’t go through high school yet, which is distracting from the content of the art being produced.
Only if it is from a limit, which it doesn’t necessarily is, and even then, it could be non-existant, exploding (can’t converge to what isn’t a number) to infinity or negative infinity. Possibly something else, but I haven’t thought of any examples
If you approach the function 1/x from the positive side then yes it *diverges* up to infinity. But if you approach x = 0 for the function 0/x it does not diverge. The actual value of any number divided by 0 is not defined and only within limits does it diverge to positive or negative infinity.
I mean 0/0 specifically is indeterminate
Multiplying anything by zero results in a number with zero size
Dividing anything by zero results in a number with infinite size
When you do both at the same time, what happens? There isn't really a good answer to that question, so we leave it as being undeterminable
And we know (2x)/x=2, so 0/0 might be 2
That's the thing, it can be anything but nothing is consistent. It cannot be defined within the usual notion of a numerical quantifier (C, sometimes C*)
[Oh no, that math wont math.](https://www.reddit.com/media?url=https%3A%2F%2Fpreview.redd.it%2F3oxkgvdhqbm71.jpg%3Fauto%3Dwebp%26s%3Ddd7000bbad862ebbb9d0bc80e60a63d340ede25b)
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0/0 is undefined. Good comic, I'm just pedantic.
Oddly enough, not quite. 4/0 is undefined, because no number times zero equals 4. But every number times zero is zero; 0/0 is indeterminate.
Only in limits. Without a limit, we say ‘undefined’
That depends on the limit For x/0 it's just undefined. For 0/x it's 0. For x/x it's 1 You can make any number you want with a "0/0" limit
Thus why 0/0 is not sufficient to determine the value of the limit, thus indeterminate
Good job Reddit! Here‘s a treat
Isn't x/0 infinity? Am I stupid??
1/x as x good to 0 from the positive side is infinity, but that's just a one sided limit x/0 it's undefined for all x because it's division by 0 (which is really multiplication by the multiplicative inverse of 0, which I'm pretty sure can only exist in fields that only contain one element, so 0=1)
undefined means that it wasn't given a definition. 0/0 isn't usually given a definition, so it is undefined. The reason why it's undefined is because there is no good way to define it, since it's an indeterminate form.
What they're getting at is there are no numbers that equals 4/0, but every number equals 0/0. That's what makes them different.
>4/0 is undefined, because no number times zero equals 4. Just wait until you learn about complex infinity
Damn you got there first
I twitched when I read that. No Work, No Life, No Math.
Prime real estate for L'Hopital's rule, though
Well technically it shouldn’t be 0/0=0 it should just be 0=0
There's a reason OP writes comics
Better to say Work = Life Work = 0 Life = 0 0 = 0
For some reason I feel like 0/0 should be 1 but I’m not smart enough to feel right
It's indeterminate, which essentially means we don't have enough information to solve the problem. This isn’t a perfect way to explain it, but try this on for size: Broadly speaking, we measure speed by seeing how far an object moves in a certain amount of time. If the car moves three meters in one second, it is moving at three meters per second - three meters divided by one second. If it moves three meters in half a second, then we have three meters divided by half a second, giving us six meters per second. Really simple, right? Let's stop time. Now, let's look at all these cars over here. They all move... zero meters... in zero seconds. How fast are they going? Are they stopped? Are they moving backwards? We have no way to know, because we're not actually measuring anything meaningful at this point. 0/0 is indeterminate. And, incidentally, x/0 (where X is not zero) is undefined because if you stop time, and one of the cars is still moving, then that doesn't make any sense. Time is stopped, so it shouldn't move at all. It's breaking the rules. Nothing makes sense anymore. You can no longer rely on this system of measurement *at all* - you can actually prove that 1=0 if you're allowed to divide by zero. So we don't allow that - we say that it's undefined, which means it's against the rules of math.
This explanation reminds me of my favorite college physics professor, thank you
Thank *you!* That's high praise!
Thing is though if it could be 1, it could also be 5, because 0 * 5 = 0, so divide both sides by 0, you get 5 = 0/0. So literally any number could be "equal" to 0/0 if we allowed 1.
It’s a good comic that would’ve been better if they didn’t make that little error. I suppose it’s generating discussion, but it makes me wonder if the author didn’t go through high school yet, which is distracting from the content of the art being produced.
Yes
Yeah, sure, until the PC breaks or becomes obsolete and you need to buy a new one XD
Or have to buy food or rent or electricity
The secret indegredient is
Dependency
Crime! The secret ingredient is always crime!
Suffering in a neo feudalist slave world
live with your parents :D
Don't threaten me with a good time.
Did you just fucking divide by zero?!
Worse, he divided zero by zero, which is undefined.
Anything divided by zero is undefined, no?
But zero divided by anything is zero... and anything divided by itself is 1
That’s only true if you’re not dividing by 0. Anything divided by 0 is undefined, including 0.
Afaik, it's infinite (or "converges to" infinite).
Only if it is from a limit, which it doesn’t necessarily is, and even then, it could be non-existant, exploding (can’t converge to what isn’t a number) to infinity or negative infinity. Possibly something else, but I haven’t thought of any examples
If you approach the function 1/x from the positive side then yes it *diverges* up to infinity. But if you approach x = 0 for the function 0/x it does not diverge. The actual value of any number divided by 0 is not defined and only within limits does it diverge to positive or negative infinity.
Came here to say that
I mean yeah, but we know that x/x is 1 so 0/0 might be a real value
I mean 0/0 specifically is indeterminate Multiplying anything by zero results in a number with zero size Dividing anything by zero results in a number with infinite size When you do both at the same time, what happens? There isn't really a good answer to that question, so we leave it as being undeterminable
And we know (2x)/x=2, so 0/0 might be 2 That's the thing, it can be anything but nothing is consistent. It cannot be defined within the usual notion of a numerical quantifier (C, sometimes C*)
“x/x = 1” is a wrong statement. the complete and actual statement is “x ≠ 0 ; x/x = 1”
If you somehow still have money to live? You won the game of life, dont keep playing
[Oh no, that math wont math.](https://www.reddit.com/media?url=https%3A%2F%2Fpreview.redd.it%2F3oxkgvdhqbm71.jpg%3Fauto%3Dwebp%26s%3Ddd7000bbad862ebbb9d0bc80e60a63d340ede25b)
"When you're unemployed there's no vacation"
No one cares, no one sympathizes You just stay home and play synthesizers
The mathematicians went fucking batshit over this comic
Great artwork and message. Thanks for sharing this!
Finding the balance is tough. Maybe set stricter work hours?
Lost my job in April. This has been my life.
Whether you have "a life" or not is up to your own interpretation.
So just die? Ok
Failed to apply L’Hopitals rule
That’s some Terrence Howard arithmetic right there
No education either huh
Math doesn't quite check out lol.
Would be better to say 0/0=1. Just don't tell that any people who work in calculus/analysis.
Grrrrrrrrr
Sorry this won't work. This is a XAND-household, we're keeping here.
It me.
Que?
0/0 is undefi-
r/technicallythetruth
As a math enjoyer I will have to execute you for the 0/0 = 0.
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this division by zero is triggering me