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. ...
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…
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.
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?
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.
You’re not teaching me anything other than things I know aren’t true on a universal level. Our taught math is completely based and adapted around smaller scale numbers and that’s why you don’t learn how infinity actually works cause for what you’ll use it it will seem correct at your scale. But not on a larger universal all-included scale. At that level you need to basically be able to grasp the actual concept of infinity,… 🤷♂️
Try doing something more than your basic calculus.
y = 1/x. Then ask the question: where does this graph touch the x axis? The answer is both + infinity and - infinity. In other words the reciprocals of + and - infinity are both zero, causing + and - infinity to look as being equal.
Another interesting way of viewing this is as follows:
Many graphs are continuous, i.e. there is one line continues without breaking. However this graph is discontinuous at the x and axes which it never meets …… until + or - infinity.
Now a way of looking at how these two separate parts of this hyperbola could join to make one continuous line would be to look at the x and y axes as being curved (with an infinite radius) to ultimately join up. If this occurred then -infinity would join up with +infinity on both axes, and the graph would be a continuous function in both vertical and horizontal directions.
In some ways it is a natural way to look at it, as it is said that space is curved anyway, so in reality + and - infinity seem to be the same thing.
Now go educate yourselves instead of insultingly arguing bs, thanks.
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…
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.
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?
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.
Says the guy who claimed infinite was ever-expanding. 😅
That’s how you approach it, with ever increasing real numbers. Take a calculus class, I’m done teaching you for free
You’re not teaching me anything other than things I know aren’t true on a universal level. Our taught math is completely based and adapted around smaller scale numbers and that’s why you don’t learn how infinity actually works cause for what you’ll use it it will seem correct at your scale. But not on a larger universal all-included scale. At that level you need to basically be able to grasp the actual concept of infinity,… 🤷♂️ Try doing something more than your basic calculus.
consider the graph below which is
y = 1/x. Then ask the question: where does this graph touch the x axis? The answer is both + infinity and - infinity. In other words the reciprocals of + and - infinity are both zero, causing + and - infinity to look as being equal.
Another interesting way of viewing this is as follows:
Many graphs are continuous, i.e. there is one line continues without breaking. However this graph is discontinuous at the x and axes which it never meets …… until + or - infinity.
Now a way of looking at how these two separate parts of this hyperbola could join to make one continuous line would be to look at the x and y axes as being curved (with an infinite radius) to ultimately join up. If this occurred then -infinity would join up with +infinity on both axes, and the graph would be a continuous function in both vertical and horizontal directions.
In some ways it is a natural way to look at it, as it is said that space is curved anyway, so in reality + and - infinity seem to be the same thing.
Now go educate yourselves instead of insultingly arguing bs, thanks.