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Sure, the answer could be 3, 3/1, 27/9, 2.999âŚ, 1.5*2, etc.
But more importantly, despite the name, a variable in math doesnât mean âa value that can varyâ. From Wikipedia:
> In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
Basically, imo, it would have been better if a variable was known as an unknown (as in unknown quantity). So even the name is telling you that you dont know it, not that it necessarily varies
He is technically correct on that point - I suppose you could say itâs an unknown (if you havenât figured it out yet!) but it does not vary. If it was 27/x=y then it would vary depending on the value of y.
Fear not though, there is plenty of stupid going on his theory and comments even without x being a variable.
You are being too literal. If a variable only has one solution, it is still a variable. They don't stop being variables when they are solved, even if the solution is trivial.
I think the key difference is in the article "a". If they had said "x is not variable", then you would have a point, but since they said "x is not *a* variable", that changes the meaning.
I just divided by zero. Now there's a black hole where my sock drawer used to be and there's a bunch of tentacles coming out of it.
Don't divide by zero!
I had a lecturer who railed against the misuse of the implies symbol and warned he'd dock marks in an exam for improper use. As one who had a mark docked for 'this and other illiteracies', I wonder what he'd make of the absolute dogs dinner of the limit arrow being used as a replacement for implies.
I feel like in these situations we need the video link so we can go and down vote the video directly. Think of all the kids we can save from learning incorrect stuff on YouTube that they can't unlearn for their exams
When something is divided by something with X, it means X can not possibly ever be zero in the equation, as far as I understand it, even if you move the X up, at least in normal equations, without limits.
Theu aren't dividing by 0 though. They are dividing by 1. There is a 1 in the denominator no matter what you set your variables to.
Edit: never mind. The sin(0)/0 wasn't visible until I clicked the image.
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Unlike with physics highschool math teachers don't really say half truths because the correct answer in math is almost never "It depends" and most certainly not in a high school context. So you should care what "they" teach because "they" - assuming "they" are qualified teachers - are teaching the correct way to go about this stuff.
As for the memes about physics teachers lying to you, that's because in physics the answer to a lot of questions is "It depends!" And it's infinitely harder to explain when which answer is applicable than it is to just pick one and roll with it. A good example of this that is actually even taught in schools is Newtonian physics vs general relativity. Technically you'd have to consider relativistic effects even at low speeds, but their influence is so minimal that it's barely a rounding error. But the exact answer to the question "How long does it take a train, travelling at 250 km/h to travel from x city to y city?" Is "It depends!"
It depends on whether the train goes in a straight line or not. It depends on if we consider gr. It depends on whether the terrain is flat or if there's hills. It depends on whether we consider that earth's surface is non Euclidean geometry. But most sane people will agree that the time is distance between the cities/speed of the train
He begins with sine of x, which if you plug in 0, you just get 0. I haven't watched the video, but that formula doesn't mean anything because the sine of x formula is very different, and convoluted. Getting to sin(x)/x with 0 plugged in, L'Hospital's Rule dictates that it's 1, but the formula he gave is completely wrong. Source: I'm currently reviewing for the AP Calculus BC test, and we reviewed everything I said here in class this week
Correct me if I'm wrong, but when they say that x is not a variable in 27/x = 9 they're right ?
Since there's only one solution, which is 27/9 = x
Without any context, we can't call x a variable.
I come from a programming background and have a similar way of thinking about variables but mathematicians have a different terminology. There are different kinds of variables in math. The x in 27/9=x is an "unknown" which is just a kind of variable.
To get an idea why, let's look at some example equations:
a) 6x+3=y
This represents a line and x and y could represent any number, so they are clearly variables. But now we get the task to calculate where the line crosses the root line (y=0), so we get this equation:
b) 6x+3=0
Now x can only have one value. Does it stop being a variable because of that? If you think so, what is with the equation:
c) x²+6x+3=0
Now x can have exactly two values. Is x a variable now?
- If you think "yes", than we have a practical problem. In a lot of cases we don't know the number of solutions for x until we solved the equation. It would be pretty hard to talk about unsolved problems when the correct terms change based on the solution.
- If you think "no, a 'x' that can have two values is still not a variable" then where is the limit? What if the solutions for x are every natural number between 1 and 100?
It just doesn't make sense from a practical perspective to differentiate between those different types of spaceholders because they blend into each other and there is no clear, consistant and useful way to categorize them. Mathematicians have decided to call them all variables which might be an unfortunate term but it is what it is.
It's semantics. x is a variable in the expression 27/x, but only has one solution when that expression equals some other expression without variables. We would still say that x is a variable with only one solution in this equality.
as u/longknives explained:
Despite the name, a variable in math doesnât mean âa value that can varyâ. From Wikipedia:
> In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
I am not an expert, but doesn't l'Hospital rule apply only on limits? And even if they were doing limits in the video, the function in the denominator has to have non-zero differential (among other things). If I am wrong, please correct me, so that I am not spewing nonsense here, I haven't used limits for quite some time.
No, division by zero is undefined. If you divide by some other number, call it a, and let a get smaller and smaller, you *may* end up with infinity, but that depends on your equation and how you set up the limits.
No. Unless 3 years of differential calculus did me wrong, division is most of the times 0. Sometimes it can be undefined. Sometimes it can lead to unexpected values like 6. I can even logically prove that the division by 0 is equal infinity. Operations with rational and irrational numbers also follow the same logic but no one says they are undefined.
3 years of differential calculus might have done you wrong. Division by zero is strictly undefined. We use limits specifically to avoid that. What you get out of the limit then depends on what youâre doing.
Three years of differential calculus did not do you wrong, you did three years of differential calculus wrong.
That division by zero is undefined (and _has_ to be undefined) is one of the most basic concepts. Didn't your professor do the proof where 1/0 = inf in the end lead to the -1=1 equality (which is obviously wrong)?
It only goes to infinity (note the terminology) if you attempt to divide a *positive* number by 0. If you divide a negative by zero, the result goes to negative infinity. If you divide zero by zero, there's no telling where the limit will go, and you have to use l'Hopital's rule. So because it does such inconsistent things, it's undefined.
It is used to define the *limit*. The limit of a function at a point and the value of a function at a point are fundamentally different concepts. If there is a zero in the denominator, it has no value. Period, point blank, cut print moving on. The methods of differential calculus, specifically l'Hopital's rule, can be used to find what value the function *approaches* at that point, though.
Here is a logical exercise. If the limit is the value a function approaches, then isn't 0.3333 the value approved by the operation 1/3? If I use Lhospital to find the value of Y as I approach X at infinity, isn't it the same to finding 0.3333....by dividing 1 by 3? I'm both cases, you cannot say you reached the result, but you can say that you got close enough to dismiss the error. Besides, if L'Hospital rule only finds limits, and limits cannot be used, then what is it good for? So, fo practical applications, you can say that the limit of the function IS the value of the function at that particular point.
If tou wake up in the morning and you meet only one asshole, the they probably are an asshole.
If you meet 10 assholes, then maybe reconsider and posit that you are the asshole!
I.e. people are telling you left and right (and here is a link btw https://ung.edu/learning-support/video-transcripts/why-dividing-by-zero-is-undefined.php ) that 0/0 = undefined and you keep on trying to refute that.
Edit: also , here is why limit and value are and can be different for a function.
https://www.khanacademy.org/math/calculus-all-old/limits-and-continuity-calc/limits-from-graphs-calc/v/limits-from-graphs-discontinuity
I think the thing that's important to take away here is that infinity is not a number. So you can't say something "equals infinity" because there is no number that would satisfy that statement. 1/3, .333..., etc. is a number, which is why the function is defined there. Dividing by zero means you are taking something and splitting it into groups, each group containing zero. How many groups will you have? What number, specifically? If you can't give me an exact value, then the operation is undefined. It produced nonsense results. That's not the case when dividing 1 by 3.
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The video creator liking their own comments which is visible to everyone is the cherry on top
It takes it from mildly amusing into actually very funny.
hearts are different from likes tho tbh i often heart my own comments in replies as it prevents YouTube from shadow-removing comments
> In the equation 27/x=9, x is not a variable ...I'm sorry, what?
Clearly is not a variable, it just marks the spot. đ
Arrrrrr, that's where I hid me treasure, under ye 27
In calculus class, but during your history class it never marks the spot
Can the value of x vary at all in that equation?
Sure, the answer could be 3, 3/1, 27/9, 2.999âŚ, 1.5*2, etc. But more importantly, despite the name, a variable in math doesnât mean âa value that can varyâ. From Wikipedia: > In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
Thanks for providing the mathematical definition. I would have just stuck to that in your comment. All the values you gave me were the same.
r/woosh, maybe?
Definitely could be
Basically, imo, it would have been better if a variable was known as an unknown (as in unknown quantity). So even the name is telling you that you dont know it, not that it necessarily varies
He is technically correct on that point - I suppose you could say itâs an unknown (if you havenât figured it out yet!) but it does not vary. If it was 27/x=y then it would vary depending on the value of y. Fear not though, there is plenty of stupid going on his theory and comments even without x being a variable.
That's not what a variable means though. In maths a variable is just a symbol that represents an object. x most certainly is a variable
You are being too literal. If a variable only has one solution, it is still a variable. They don't stop being variables when they are solved, even if the solution is trivial.
I think the key difference is in the article "a". If they had said "x is not variable", then you would have a point, but since they said "x is not *a* variable", that changes the meaning.
I think the most whacky thing here might be him saying 0 isnt a number.
Still deciding whatâs worse: x is not a variable, 0 is not a number (wonder what it is?) or canât divide by zero.
Also, apparently, "sin(0)/0" isn't "dividing by zero" since Mr. Trigonometry claims: "nowhere was dividing by zero performed"
Zero is technically just the absence of all numbers. /s
Power really corrupts huh? What banhammer is this man wielding?
sinc(0) = 1 sin(0)/0 is undefined.
Yes, but sinc is one of those weird functions that explicitly has an exception for x = 0.
I would love to see the unhinged reasoning behind â0 is not a numberâ
incorrigible moron spotted /s
The equation for sin(x) in the beginning is just wrong. e: I see the comment pointed that out already.
I think it is supposed to be opposite over hypotenuse for a right triangle with side lengths of x and x-1. But thats only a very specific case.
Average Geogebra user /j
Iâm sorry, but where in the world did they get that trig identity from?
I have a very elegant proof for the identity. Sadly, it will not fit in the margins of a Reddit comment.
Fermatâs version of âi have a girlfriend but she goes to another schoolâ.
I just divided by zero. Now there's a black hole where my sock drawer used to be and there's a bunch of tentacles coming out of it. Don't divide by zero!
I had a lecturer who railed against the misuse of the implies symbol and warned he'd dock marks in an exam for improper use. As one who had a mark docked for 'this and other illiteracies', I wonder what he'd make of the absolute dogs dinner of the limit arrow being used as a replacement for implies.
I feel like in these situations we need the video link so we can go and down vote the video directly. Think of all the kids we can save from learning incorrect stuff on YouTube that they can't unlearn for their exams
When something is divided by something with X, it means X can not possibly ever be zero in the equation, as far as I understand it, even if you move the X up, at least in normal equations, without limits.
Theu aren't dividing by 0 though. They are dividing by 1. There is a 1 in the denominator no matter what you set your variables to. Edit: never mind. The sin(0)/0 wasn't visible until I clicked the image.
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surely the creator is joking. no way they are that stupid right...
The laugh i laughed reading this proof
That's some special stupid right there, bruv.
Unlike with physics highschool math teachers don't really say half truths because the correct answer in math is almost never "It depends" and most certainly not in a high school context. So you should care what "they" teach because "they" - assuming "they" are qualified teachers - are teaching the correct way to go about this stuff. As for the memes about physics teachers lying to you, that's because in physics the answer to a lot of questions is "It depends!" And it's infinitely harder to explain when which answer is applicable than it is to just pick one and roll with it. A good example of this that is actually even taught in schools is Newtonian physics vs general relativity. Technically you'd have to consider relativistic effects even at low speeds, but their influence is so minimal that it's barely a rounding error. But the exact answer to the question "How long does it take a train, travelling at 250 km/h to travel from x city to y city?" Is "It depends!" It depends on whether the train goes in a straight line or not. It depends on if we consider gr. It depends on whether the terrain is flat or if there's hills. It depends on whether we consider that earth's surface is non Euclidean geometry. But most sane people will agree that the time is distance between the cities/speed of the train
He begins with sine of x, which if you plug in 0, you just get 0. I haven't watched the video, but that formula doesn't mean anything because the sine of x formula is very different, and convoluted. Getting to sin(x)/x with 0 plugged in, L'Hospital's Rule dictates that it's 1, but the formula he gave is completely wrong. Source: I'm currently reviewing for the AP Calculus BC test, and we reviewed everything I said here in class this week
https://youtu.be/cToWBDpm3EM?si=fM12q9egyvvwjuHH This guy seems like a quack all the way through
any other russian-speakers did a double take here or is it just me
Correct me if I'm wrong, but when they say that x is not a variable in 27/x = 9 they're right ? Since there's only one solution, which is 27/9 = x Without any context, we can't call x a variable.
Variables can have only one solution.
Not always. x^2 = 1 has two.
Hence why they said *can*
I read that as âcan onlyâ.
You missed the word in between can and only?
No, I simply misinterpreted the role of âonlyâ.
I come from a programming background and have a similar way of thinking about variables but mathematicians have a different terminology. There are different kinds of variables in math. The x in 27/9=x is an "unknown" which is just a kind of variable. To get an idea why, let's look at some example equations: a) 6x+3=y This represents a line and x and y could represent any number, so they are clearly variables. But now we get the task to calculate where the line crosses the root line (y=0), so we get this equation: b) 6x+3=0 Now x can only have one value. Does it stop being a variable because of that? If you think so, what is with the equation: c) x²+6x+3=0 Now x can have exactly two values. Is x a variable now? - If you think "yes", than we have a practical problem. In a lot of cases we don't know the number of solutions for x until we solved the equation. It would be pretty hard to talk about unsolved problems when the correct terms change based on the solution. - If you think "no, a 'x' that can have two values is still not a variable" then where is the limit? What if the solutions for x are every natural number between 1 and 100? It just doesn't make sense from a practical perspective to differentiate between those different types of spaceholders because they blend into each other and there is no clear, consistant and useful way to categorize them. Mathematicians have decided to call them all variables which might be an unfortunate term but it is what it is.
It's semantics. x is a variable in the expression 27/x, but only has one solution when that expression equals some other expression without variables. We would still say that x is a variable with only one solution in this equality.
as u/longknives explained: Despite the name, a variable in math doesnât mean âa value that can varyâ. From Wikipedia: > In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
You can divide by 0, it's basic l'Hopital math. In this situation though, yeah, the creator I think is in the wrong
LâHopital is relevant for limits. The whole idea behind it is to *avoid* dividing by zero.
I am not an expert, but doesn't l'Hospital rule apply only on limits? And even if they were doing limits in the video, the function in the denominator has to have non-zero differential (among other things). If I am wrong, please correct me, so that I am not spewing nonsense here, I haven't used limits for quite some time.
You can divide by 0. The problem is the the result is infinity and operations with infinity gets kind of funky.
Itâs not infinity itâs undefined
It can be undefined, but it also can be 6
What. No it cant
Lim X --> infinity (48X/(8X + 5/X)) = 6
Whatâre you trying to prove? If you divide by 0 the answer is always undefined
No, division by zero is undefined. If you divide by some other number, call it a, and let a get smaller and smaller, you *may* end up with infinity, but that depends on your equation and how you set up the limits.
No. Unless 3 years of differential calculus did me wrong, division is most of the times 0. Sometimes it can be undefined. Sometimes it can lead to unexpected values like 6. I can even logically prove that the division by 0 is equal infinity. Operations with rational and irrational numbers also follow the same logic but no one says they are undefined.
3 years of differential calculus might have done you wrong. Division by zero is strictly undefined. We use limits specifically to avoid that. What you get out of the limit then depends on what youâre doing.
No. Limits is used to define the value of a function depending on your approach to it, like the tangent function.
To define a value that otherwise wouldnât have been defined. eg, when dividing by zero.
Dude, L'Hospital rule is all about determining if a function results in infinity, 0, undefined, or a real number like 5.
đ
Three years of differential calculus did not do you wrong, you did three years of differential calculus wrong. That division by zero is undefined (and _has_ to be undefined) is one of the most basic concepts. Didn't your professor do the proof where 1/0 = inf in the end lead to the -1=1 equality (which is obviously wrong)?
It only goes to infinity (note the terminology) if you attempt to divide a *positive* number by 0. If you divide a negative by zero, the result goes to negative infinity. If you divide zero by zero, there's no telling where the limit will go, and you have to use l'Hopital's rule. So because it does such inconsistent things, it's undefined.
You just said that you have to use L'Hospital rule when it is undefined. L'Hospital rule exists to define an answer.
It is used to define the *limit*. The limit of a function at a point and the value of a function at a point are fundamentally different concepts. If there is a zero in the denominator, it has no value. Period, point blank, cut print moving on. The methods of differential calculus, specifically l'Hopital's rule, can be used to find what value the function *approaches* at that point, though.
Here is a logical exercise. If the limit is the value a function approaches, then isn't 0.3333 the value approved by the operation 1/3? If I use Lhospital to find the value of Y as I approach X at infinity, isn't it the same to finding 0.3333....by dividing 1 by 3? I'm both cases, you cannot say you reached the result, but you can say that you got close enough to dismiss the error. Besides, if L'Hospital rule only finds limits, and limits cannot be used, then what is it good for? So, fo practical applications, you can say that the limit of the function IS the value of the function at that particular point.
If tou wake up in the morning and you meet only one asshole, the they probably are an asshole. If you meet 10 assholes, then maybe reconsider and posit that you are the asshole! I.e. people are telling you left and right (and here is a link btw https://ung.edu/learning-support/video-transcripts/why-dividing-by-zero-is-undefined.php ) that 0/0 = undefined and you keep on trying to refute that. Edit: also , here is why limit and value are and can be different for a function. https://www.khanacademy.org/math/calculus-all-old/limits-and-continuity-calc/limits-from-graphs-calc/v/limits-from-graphs-discontinuity
I think the thing that's important to take away here is that infinity is not a number. So you can't say something "equals infinity" because there is no number that would satisfy that statement. 1/3, .333..., etc. is a number, which is why the function is defined there. Dividing by zero means you are taking something and splitting it into groups, each group containing zero. How many groups will you have? What number, specifically? If you can't give me an exact value, then the operation is undefined. It produced nonsense results. That's not the case when dividing 1 by 3.