this post was submitted on 06 Dec 2023
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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.
Boundless and endless (and the fact it's larger than any number) doesn't mean it's ever-growing. It already is.
Right! hence why you can only approach it with the limit notation, never operate on it directly. Please, take a calculus class. You might even learn this on day 1
Again, I did... If I could argue all this out of pure imagination, now that would be something...
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.
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?
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...
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
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.
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.
My guy, not only are you wrong but the more you try to explain yourself the more you are revealing you don't understand the subject. The evidence you are bringing up is supporting the premise of infinity not being a value. You are coming to the exact wrong conclusion.
I have a BA in mathematics and a masters in teaching mathematics. I am highly qualified to speak on this. Trust me, you're wrong.
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.
This. 1/0 does not exist in our number system. Alternate number systems allow 1/0 to exist at the expense of many useful properties of mathematics that (OC?) OP doesn’t seem to understand. Not everything in math has to make sense: we simply gave ourselves some set rules, and then built up a system off the consequences of those rules. If 1/0 cannot exist within those rules, then that’s it. If you’re going to argue against centuries of mathematical advancements then so be it, I can’t stop you, but it’s pretty obviously a losing battle.
Dude you picked an obscure sub field of mathematics defined by looping a set around a sphere in order to make both positive and negative infinity equal. That's like saying sea food is bad because I asked something allergic to shell fish if they like it.
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?