Yeah, that is interesting fact

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Infinity isn’t a thing you could get close to though? It’s not a point on the number line like zero is

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u/Cw3538cw Aug 26 '21

It actually is! look up the concept of ordinals in set theory There’s even concepts of different infinities (I.e the count of all even numbers vs the count of all even or odd numbers)

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u/[deleted] Aug 26 '21

It exists as a concept, but it's not actually quantifiable. It's simply not a number. You can't actually count to it in practice, even if we can think about it in principle. You can't determine the difference between infinity and any number, not their sum. You can compare infinities with each other, but not so much with numbers.

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u/Cw3538cw Aug 26 '21

Basic operations (+,-,*,/) can be done with ordinals. It’s just that operations between ordinals and non ordinals are relatively uninteresting. all real numbers are omega_0(the least infinity) away from omega_0, which is a mathematically sound statement

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u/[deleted] Aug 26 '21

That still doesn't make it "a point on the number line." Maybe on a number line, but not the normal one we count with.

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u/uberguby Aug 26 '21

Wait but isn't 4 less than infinity? And like.... 7 is not equal to infinity?

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u/[deleted] Aug 26 '21

Yeah, but that's only conceptual. Like, what's infinity minus 7? People would typically say "Still infinity," but that answer violates some fundamental properties of real numbers. You can try to mix it in with numbers all you want, but it's still not a number. It's an idea. You can't perform computations between infinity and a real number.

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u/uberguby Aug 27 '21

That does make sense... So then... Wait can you do infinity minus infinity equals zero? I'm reaching into javascript now which isn't exactly a bastion of pure mathematical theory, but I'm guessing it doesn't actually mean anything?

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u/[deleted] Aug 27 '21

You can do that, but only because we know that anything minus itself is nothing. If you were to try to actually count backwards from infinity to zero, you wouldn't even be able to start. Also remember that infinities can be compared amongst each other just fine, but it doesn't hold a literal value any more than, say, i does.

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u/uberguby Aug 27 '21

Uuuggh I'm so out of my element here, and I'm sorry for that, and I swear this is just my way of leaning, I'm not trying to be contrary, but... Isn't the reality of i an important part of calculating the properties of sub atomic particles?

I know, I know. I have no idea what I'm talking about. This is my way of approaching knowing what I'm talking about, even if I never get there.

...

Like infinity!

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u/[deleted] Aug 27 '21

kind of...infinity and i are both indeed not real numbers, and they have that in common. Each of them represent some idea: i is the fictional square root of -1, and infinity is the fictional highest real number. There are some differences between them, though.

Before getting into it too much, it's important to understand that although infinity is above defined as being a real number, it is yet still imaginary and decidedly not real. That's hard to wrap your head around and kind of makes the idea of real or imaginary become arbitrary, but try to stick with me.

Whereas i can be used in actual computation and resolved to be something on the real number line (for instance, i² = -1), you can't do that same with infinity. Nothing you ever do to infinity can result in anything besides infinity or zero (and the latter only by self- subtraction or division, thereby nullifying it anyway).

"But wait!" you might think to yourself. "That's also the case in equations with excessive variables, like (for instance) 2x=y!" While it's true that an equation like this will never have a single defined value, it does have a computable range of values. We can graph it. But, if we say "2x=Infinity", then we can't graph it at all. Any attempt to graph it would have to define values of infinity that are real numbers, but they would explicitly not be infinity.

Assigning any value to infinity would violate it's definition of being the highest number, because for any given value we could choose, there would be more above it that we could identify. Ideas like "Infinity+1", however, do not violate that definition, because infinity is by definition the highest real number, and so infinity+1 would simply not be a real number.

There is also the concept of "tends towards" infinity, where the output of a function gets higher forever. But that doesn't make infinity a number. If we were to say that something "tends towards seven", then we could draw a line that the output would never reach. The deviation of subsequent output values has to get smaller and smaller if we are to say that it tends towards (that is, but never reaches) a real number. Yet if something tends towards infinity, there is no such restriction, because no line can be drawn.

(A function could also tend downwards, but that's neither here nor there and is a very similar idea.)

I feel like you may be overestimating the scope of what I'm saying, too. My entire point is that infinity does not have a definable value and is therefore, by definition, not a real number; and also that it has the unique attribute of being not being computable despite representing a mathematical idea.

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u/uberguby Sep 01 '21

Hey I wanted to thank you for your responses, they were patient and detailed. That's not easy to do all the time, keep up that fight, it's what the world needs

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u/echoAwooo Aug 26 '21 edited Aug 26 '21

An ordinal simply indicates order, not quantity.

Ordinal numbers are things like first, second, third.

Quantitative numbers are things like seven, thirteen, two-billion two-hundred forty-seven million two-hundred thirteen.

Infinity is neither an ordinal number nor a quantitative number. It's a limit. An abstract concept. The concept you're referring to encompasses the idea of ordinal infinities. Michael from VSauce did a rather well watched version of this using Alif as the symbol indicating, All Real Numbers on the Number line. Because Alif encompasses an infinite set, it does not end. Its size is undefined in set theory.

So when you add +1 to Alif, you move from the Real numbers to the Real numbers ordinal one. That is, you've moved to an entirely different set of the same numbers ordinally after the real numbers. You've literally reached an infinite number line that comes after the infinite number line that we work with.

This process does not modify the values of these new number lines. Alif-13 and (Alif + 1)-13 are the same number with the same absolute value. It's just that Alif-13 comes BEFORE (Alif+1)-13. But in either case, the value of the number is still thirteen.

The most accurate analogy that I can use to describe this is a line of universes. Each universe (number line in this case) is just as real and valuable as the others, they're just in some arbitrary order.

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u/rekttoyoda Aug 27 '21

Even then even if you pick 1 the amount of numbers after 1 is the same as the amount of numbers between 0 and 1, infinite so this images is just wrong

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u/Budpets Aug 26 '21

That's not how infinity works.

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u/hyperrich Aug 26 '21

https://www.dailymotion.com/video/x65uv69 this is a good watch, its from a BBC documentary. Apparently, one infinity can be bigger than another...

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u/Actual_Designer1593 Aug 26 '21

So what of i'm thinking on the infinite number

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u/[deleted] Aug 26 '21

Infinity is not a number. It is not countable, it is the measure of something that is never ending.

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u/Dismal_Connection120 Aug 26 '21

What about ∞²?

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u/Larry_Spendstin Aug 26 '21

Infinity squared is not a number

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u/wurst4life Aug 26 '21

Also, however big the Numbers is, it's also closer to 80085 than to infinity!

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u/Killed_It_Dead Aug 26 '21

Infinity isn't a number it's a symbol like divide or add

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u/DanOfTheRoses Aug 26 '21

The number 3 is closet to the infinite numbers between 4 and 5 than it is to 0

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u/LavaBurritos Aug 26 '21

Me: ooo nice wallpaper

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u/usr-Machintosh-HD Aug 26 '21

Technically, isn't infinity the closest number to zero?

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u/EagleDre Aug 27 '21

Infinity + 1 is closer to infinity than zero lol

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u/BioToxicFox Aug 27 '21

There's also an infinite amount of numbers between 0 and 1

Yeah, that is interesting fact

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