I saw this Reddit post today saying "My son's third-grade teacher taught my son that 1 divided by 0 is 0. I wrote her an email to tell her that it is not 0. ...
the limit of y in 1/x=y as x approaches 0 from negative one is negative infinity. the limit as x approaches 0 from positive one is positive infinity. 1/0 is simultaneously both positive and negative infinity and is paradoxical.
One could argue that negative and possitive infinity, unlike natural numbers, boils down to the same thing, though. Just like 0, infinity technically has no + or -.
Don’t think of infinity as a value. It’s more of a concept to explain numerical behavior. What you described would be like running north at 5 mph south. The limit diverge do it does not exist.
But it is a value. Just one we tend to avoid by claiming it doesn’t exist or is impossible…
Our minds just have a hard time imagining it, but that doesn’t mean it doesn’t exist.
Our minds? Infinity isn’t something we don’t understand - we invented the concept of infinity. The mathematics community agreed on its definition, which includes the fact that infinity is not a real number, it literally does not exist. Show me infinity, I’ll give you infinity+1.
You deciding that infinity means something else is not a math problem but a language problem, so if being right about this is that important to you, start a petition or something
First sentence from Wikipedia: “Infinity is something which is boundless, endless, or larger than any natural number.”
In other terms give me a natural number n, I’ll show you a larger number, n+1, and I’ll do it again and again. That’s the definition of infinity. There’s always a bigger number.
No, it’s not a value. It’s defined as not being a value. No after how much you bend and break maths, infinity will never be a value. Why do you keep telling people wrong things?
It is explicitly not a value. The reason you cannot perform arithmetic on infinity is because it has no value. It has cardinality but that is not unique. The set of all integers is infinite as is the set of all real numbers but they have different cardinality as integers are countably infinite whereas real numbers are not countable infinite.
I’d only break argumentative math, not actual calculatable math…
Unlike many always say, math has too many agreements and ‘definitions’ and things we added to be universal. On a universal level infinite solves the +/- by the fact it’s infinite…
Okay, so what? Breaking useful things is bad, no matter what group they belong to. What is positive about no longer being able to use L’Hopital’s rule?
Quora has many dubious answers. I wouldn’t use it for any point of argument.
Infinity is not a number. It’s a concept. You’ll find yourself in many paradoxes if you start treating infinity as a number (you can easily prove that 1 = 2 for example).
By your argument, is 1/|x| negative infinity when x is 0? The expression is strictly positive, so it doesn’t make sense to assign it a negative value. But your version of infinity would make it both positive and negative.
Another one: try to plot y = (x^2 - 1) * 1/(x - 1). What happens to y when x approaches 1? If you look at a plot, you’ll see that y actually approaches 2. What would happen if we treat 1/(1-1) as your version of infinity? Should we consider that y could also approach -2, even if it doesn’t make any sense in this context?
Curious I found something that proofs my whole point exactly to the letter though… I must be exactly the same kind of wrong as that other person that actually drew you the circle with it as proof…
The page clearly states this is a non-standard number system. You cannot use it in the general case. It is a common practice for mathematicians to come up with new number systems with new rules and see where it leads to. Maybe there’s a practical use for it?
This is the same case here. Some mathematician came up with a new number system where 1/0 is treated as a new number with special properties and see what it leads to. Any new conclusion made in this number system is probably not applicable in any standard number system.
Similarly this is a number system that has been constructed such that infinity exists as a number, but in this case negative infinity is a distinct number. 1/0 is not defined under this system as a result. This is a non-standard system as well, so shouldn’t be used unless it’s clearly intended.
It breaks calculus, the math that made your phone and has a billion other uses. Directionality of infinities is critical. In calculus, infinity refers only to the magnitude of the resulting vector. Because I suspect you don’t know, integers are a 1-dimensional vector.
No but some of the values/specs were calculated by summing an infinite number of infinitely small values. Take a calculus class brother, it’s a cool subject if you’re interested in infinity
I kinda already did many, though. Do you honestly think I argue math from my own imagination? Not sure I can do that while remaining logical ánd finding exactly the same info online if I look it up, cause that would be kinda amazing.
You did many. Well, yeah, I honestly don’t believe you as a matter of fact. By our conversation: You don’t seem to know what a limit is, you don’t know the difference between natural and real numbers, you don’t know the formal definition of infinity, and you don’t know any applications of calculus, the subject built around that definition. So yeah, I have a really hard time believing that you’ve ever taken a college level math class, or even paid good attention in your highschool math classes either.
the limit of y in 1/x=y as x approaches 0 from negative one is negative infinity. the limit as x approaches 0 from positive one is positive infinity. 1/0 is simultaneously both positive and negative infinity and is paradoxical.
One could argue that negative and possitive infinity, unlike natural numbers, boils down to the same thing, though. Just like 0, infinity technically has no + or -.
Don’t think of infinity as a value. It’s more of a concept to explain numerical behavior. What you described would be like running north at 5 mph south. The limit diverge do it does not exist.
But it is a value. Just one we tend to avoid by claiming it doesn’t exist or is impossible… Our minds just have a hard time imagining it, but that doesn’t mean it doesn’t exist.
Our minds? Infinity isn’t something we don’t understand - we invented the concept of infinity. The mathematics community agreed on its definition, which includes the fact that infinity is not a real number, it literally does not exist. Show me infinity, I’ll give you infinity+1.
You deciding that infinity means something else is not a math problem but a language problem, so if being right about this is that important to you, start a petition or something
So you believe the universe just ends somewhere with nothing behind it?
What’s that got to do with anything? Infinity is just shorthand for “ever-increasing number”.
Uhm… No it’s not… 🤨
First sentence from Wikipedia: “Infinity is something which is boundless, endless, or larger than any natural number.”
In other terms give me a natural number n, I’ll show you a larger number, n+1, and I’ll do it again and again. That’s the definition of infinity. There’s always a bigger number.
No, it’s not a value. It’s defined as not being a value. No after how much you bend and break maths, infinity will never be a value. Why do you keep telling people wrong things?
It is explicitly not a value. The reason you cannot perform arithmetic on infinity is because it has no value. It has cardinality but that is not unique. The set of all integers is infinite as is the set of all real numbers but they have different cardinality as integers are countably infinite whereas real numbers are not countable infinite.
If you were to argue this, you’d suddenly break a lot of useful maths. So why would you do so?
I’d only break argumentative math, not actual calculatable math…
Unlike many always say, math has too many agreements and ‘definitions’ and things we added to be universal. On a universal level infinite solves the +/- by the fact it’s infinite…
Okay, so what? Breaking useful things is bad, no matter what group they belong to. What is positive about no longer being able to use L’Hopital’s rule?
Infinite is not calculable math. If you use infinity in your calculations you will get slapped on the wrists by a math professor.
Google is your friend. I’m gonna leave this here and stop arguing about infinity to people that obviously have no understanding of it.
Quora has many dubious answers. I wouldn’t use it for any point of argument.
Infinity is not a number. It’s a concept. You’ll find yourself in many paradoxes if you start treating infinity as a number (you can easily prove that 1 = 2 for example).
By your argument, is 1/|x| negative infinity when x is 0? The expression is strictly positive, so it doesn’t make sense to assign it a negative value. But your version of infinity would make it both positive and negative.
Another one: try to plot y = (x^2 - 1) * 1/(x - 1). What happens to y when x approaches 1? If you look at a plot, you’ll see that y actually approaches 2. What would happen if we treat 1/(1-1) as your version of infinity? Should we consider that y could also approach -2, even if it doesn’t make any sense in this context?
Curious I found something that proofs my whole point exactly to the letter though… I must be exactly the same kind of wrong as that other person that actually drew you the circle with it as proof…
C’mon, now you’re just reaching.
The circle is just a visualization of a concept, not a proof. The Quora answer clearly refers to this concept: https://mathworld.wolfram.com/ProjectivelyExtendedRealNumbers.html
The page clearly states this is a non-standard number system. You cannot use it in the general case. It is a common practice for mathematicians to come up with new number systems with new rules and see where it leads to. Maybe there’s a practical use for it?
This is the same case here. Some mathematician came up with a new number system where 1/0 is treated as a new number with special properties and see what it leads to. Any new conclusion made in this number system is probably not applicable in any standard number system.
The article also mentions this number system: https://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html
Similarly this is a number system that has been constructed such that infinity exists as a number, but in this case negative infinity is a distinct number. 1/0 is not defined under this system as a result. This is a non-standard system as well, so shouldn’t be used unless it’s clearly intended.
It breaks calculus, the math that made your phone and has a billion other uses. Directionality of infinities is critical. In calculus, infinity refers only to the magnitude of the resulting vector. Because I suspect you don’t know, integers are a 1-dimensional vector.
Nothing in my phone is either infinite, nor negative.
No but some of the values/specs were calculated by summing an infinite number of infinitely small values. Take a calculus class brother, it’s a cool subject if you’re interested in infinity
I kinda already did many, though. Do you honestly think I argue math from my own imagination? Not sure I can do that while remaining logical ánd finding exactly the same info online if I look it up, cause that would be kinda amazing.
You did many. Well, yeah, I honestly don’t believe you as a matter of fact. By our conversation: You don’t seem to know what a limit is, you don’t know the difference between natural and real numbers, you don’t know the formal definition of infinity, and you don’t know any applications of calculus, the subject built around that definition. So yeah, I have a really hard time believing that you’ve ever taken a college level math class, or even paid good attention in your highschool math classes either.