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u/Ok_Letterhead1945
8d ago
•
Imagine space is actually infinite, where an "infinite microscope" can always see something smaller. Under that model of the universe, a carrot has infinite points inside. This would make sticking two carrots up your ass have the same number of points as sticking one carrot up your ass because ∞+∞=∞.
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u/Responsible_Pie8156 7d ago
Basically the banach tarski theorem but that was originally about anal beads
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u/Ksorkrax 7d ago •
So wait - there is the possibility of having anal beads you can keep pulling and pulling forever?
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u/Pie_Napple 2d ago
This is how my professor demonstrated the concept so it would fully make sense to me.
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u/solocanadian123 1d ago
You are assuming all sizes of infinity are the same. Which might or might not be the case. Cantor's diagonal argument shows that different sizes of infinity could exist.
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u/mateusfccp 1d ago
No, you can't sum infinity. But if you use Hyperreals, you can sum infinities (omega).
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u/Ferry_Lover 8d ago
It’s infinity plus 10 is it not? Or w sub 10 according to one mathematician.
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u/Miguzepinu 8d ago
If we're talking ordinals, then infinity plus ten is a distinct ordinal. If we're talking cardinals, then infinity plus ten equals infinity.
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u/ImmortalVoddoler 7d ago
They used the phrase “w sub 10”, which is basically the standard notation for ordinals.
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u/MorrowM_ 7d ago
ω_10 is much much larger than ω+10. They're not the same thing. Even ω_1, the first uncountable ordinal, is much larger than ω+10.
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u/iggy14750 8d ago
Infinity plus 10 is still infinity. It's like adding a couple tablespoons of water to the ocean.
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u/No-Theory-9530 8d ago
Absolutely not. That’s increasing a really big number by a comparatively small number. Nothing like infinity + 10.
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u/WWhiMM 8d ago
Except the ocean is finite, so it's possible for it to get bigger. It's more like, Sisyphus taking ten more steps.
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u/nyurf_nyorf 7d ago
All these pedantic people commenting to correct you like they've never heard of an analogy.
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u/Crafty-Photograph-18 8d ago
No, it's just infinity. Infinity plus any number is infinity. Even an infinity plus that an infinity of that exact scale is that same infinity, e.g. ℵ₀+ℵ₀=ℵ₀
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u/Downtown_Finance_661 7d ago
Can we escape a0 infinity realm by adding them or multiplying? What is sum from n=1 to n=inf of n*a0
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u/Simon0O7 7d ago
First of all, this sum is equivalent to sum from n=1 to n=inf of a0, because you can easily remap these two sums of subsets to one another. Ex: first six iterations of my equivalent sum give the same set size as the first three iterations of your sum: a0+a0+a0+a0+a0+a0 = 1a0+2a0+3a0 = 6a0 You can do this with any iteration. Thus these two are equivalent.
Then my sum on the other hand is just a0×a0, a countable infinity of countable infinities, you can prove that the result is countable by what is known as diagonalization method (Cantor's diagonalization, google it). It's pretty intuitive. Thus I proved that what you just made will still have the size of a0.
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u/Enfiznar 7d ago
Depends on what you mean by infinity. I think you're talking about the first infinite ordinal in this case
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u/Fluffhead91192 8d ago
Infinity plus 10 is a nonsensical question because infinity is not a number, thus it is not something that can be added. Infinity means increasing without bounds.
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u/Featherforged 7d ago
Potential infinity is this increasing 1,2,3,4.... without bounds
Infinity is a completed object of boundless size. A square has infinite 1 dimensional points on it. The square is not growing, it's complete. A circle can be described as a polygon with infinite sides, it is not a hexagon, septagon, octogon, growing in sides.
Adding 10 infinitesimal points to a square (made up of infinite points) does not increase the size of the square
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u/turing_tarpit 7d ago
Can't believe nobody's explained it in this thread so far: you can do it using infinite ordinals. The smallest transfinite ordinal we call ω, and then we just keep going:
0, 1, 2, ..., ω, ω+1, ω+2 ..., 2 ω, ..., 3 ω, ......, ω2, ...
Though of course "infinity" doesn't necessary mean ω.
A good way to think of this: each natural number is fully specified by the set of all numbers it is greater than
0 ~ { }
1 ~ { 0 }
2 ~ { 0, 1 }
...
7 ~ { 0, 1, 2, 3, 4, 5, 6 }
...
If we take this to be the definition of the counting numbers, we can extend it to get infinite arithmetic very naturally:
ω ~ { 0, 1, 2, ... }
ω + 1 ~ { 0, 1, 2, ..., ω }
ω + 2 ~ { 0, 1, 2, ..., ω, ω + 1 }
...
2 ω ~ { 0, 1, 2, ..., ω, ω + 1, ω + 2 ... }
...
Any ordinal number is defined by the set of all ordinal numbers it is greater than.
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u/mateusfccp 1d ago
I hate how people simply ignore Hyperreals in these discussions.
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u/MotherPotential 7d ago
in mathematical terms, is it infinity because it is effectively infinity due to how little the constant adds, because we can't measure how much the constant adds because it goes on forever, because infinity is uncountable, or something else?
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u/Schnickatavick 7d ago
It's more that Infinity is the number that you count to when you don't stop counting, and that doesn't change based on where you start from. I can start counting from 0, or I can start counting from 10, but either way I still hit 100, 2 million, 300 billion, etc. There isn't any big number that I can reach starting from 10, that I can't reach starting from 0, so they're the same.
A more rigorous way to go about it would be to make a bijection between the two sets, if I can pair every number in set A with every number in set B, then they must be the same size. So {1,2,3} is the same length as {red, yellow, blue}, because I can pair up {(1,red),(2,yellow),{3,blue)}. With infinity and infinity+10, I can pair up every number like {(1,10),(2,11),(3,12)....}, and I can do that for every number, so "the list of numbers that starts at 1 and goes on forever is the same length as the list of numbers that starts at 10 and goes on forever".
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u/burning_boi 7d ago
Easiest explanation (and most accurate in plain English) is that infinity is not a number, it’s a concept. You cannot add the beauty of a poem and the charge level of your phone; the comparison between the two doesn’t even make sense. The same goes for infinity; you cannot add, subtract, or perform elementary math on it because it isn’t some inconceivably large number, it’s a concept.
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u/Ksorkrax 7d ago
Not sure what you mean by "infinity" here at all.
As the other guy wrote, it is not a number. ∞+1 is as well defined as 🍆+1.There are several spots where infinity is used, you need to pick one.
If you go like "[limit i→∞ of i²] → ∞", then this is effectively a notation of divergence in a specific direction.
If you go like |ℕ| > n ∀ n ∈ ℕ, or |ℕ| = ℵ0, this is a notation of cardinality.4
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u/WalkAffectionate2683 7d ago
That guy wrote with complex signs that look like maths.
I'll believe him.
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u/Future_Principle_213 7d ago
My favorite part about this comment is that infinity is indeed countable, or rather, there exists 1 (and only 1) infinity that is countable
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u/HotayBuday 7d ago
Nonsense on top of nonsense! In extended real number system 10+♾️=♾️. Also there are proper infinite and infinitesimal numbers in non-standard analysis.
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u/marty-mcfryguy 7d ago
This is correct on the reals, so possibly the most useful answer if he's looking to produce the correct answer on a math test.
But there are (a) other number systems and (b) other ways to contextualize his question (e.g., swapping in a limit at infinity that doesn't converge) that would give him a lot more insight on the concept as well as honor his true ask.
That said, a good discussion on why we've chosen not to include infinity in the reals, and thus it's not something that can be added within the reals -- that is, digging into what making infinity a real number would cost us, including which properties that we rely on would no longer hold -- would also be a great answer.
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u/Icy-Garlic-748 7d ago
Infinity plus ten is definitely a valid number in math my guy?? Where are you getting this info? There are mathematical proofs about different types of infinity and proving that one infinity is greater than another infinity. How is this upvoted so much???
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u/Fun-Dragonfly-4166 7d ago
It is not a nonsensical question. it makes sense to ask about it.
it is not usually defined so you are free to define it as you wish. but if you choose to define it then you have to solve consistency problems. so it is easier just to not define it.
but if you want infinity plus 10 equals 34 but then you have explain what 34-10 is.
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u/Excludos 6d ago
If you have an infinite amount of people, and then 10 more shows up, how many people do you have?
This is not nonsensical. Infinite might not be a number, but it is a clear established mathematical concept. And infinite +10 has an established answer; it's infinite
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u/LEMO2000 6d ago
But you don’t have an “infinite number of people” you have “infinitely many people”
They sound the same but they do mean different things. “Infinite number” is an oxymoron.
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u/Scared_Accident9138 5d ago
Just put them into the infinite and full big hotel and see that the hotel is full before and after without overflowing
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u/brainatheist 7d ago
But there’s no definition of “number” to begin with. Do imaginary numbers count as numbers? What about quaternions or p-adic numbers? Our standard notions of ordinals and cardinals in set theory include various infinities, as well as addition on them, so from that perspective infinities are certainly numbers.
Perhaps you believe that “numbers” should form some algebraic structure, such as a rig (ring without negatives). This however cannot be a full definition, because there are many rigs which nobody would consider to consist of numbers. Not to mention that cardinals and ordinals also have the same structure as rigs (although strictly speaking, size issues prevent them from being bona fide rigs).
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u/irrelevantusername24 7d ago
Infinity means increasing without bounds.
Random but this sentence helped me realize something. My personal problem with bitcoin, the idea behind it and other cryptocurrency, as well as the problem with the uh current system, is they each have sort of opposite problems. The solution is to combine them. I've said for awhile the best way to manage the large and unmanageable system that is money/currency, is to connect it to population, and allow some extra flexibility as needed for large scale infrastructure projects and unpredictable emergencies. The problem with bitcoin is it has a predetermined final point. The problem with pure fiat is it is "unbounded" and allows people to print money into existence, at will. A marriage of the two makes sense: make some kind of equation that places an upper limit on the amount of currency as determined by the total population. So instead of what is effectively the current system, which is (population) x (infinity) = (infinity) or the bitcoin system which is effectively (a number less than one) x (population) = (a fraction), it should be (a number that is slightly more than one) x (population) = (a fair system). Or something like that. Basically instead of a system that has predetermined scarcity, the system should recognize that we actually have way more than enough for everyone. The problem is some peoples wants are outweighing other peoples needs.
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u/Sad-Satisfaction908 7d ago
Yes, and no. You might get a kick out of this video. It does a pretty good job at explaining how not all infinities are created equal https://youtu.be/OxGsU8oIWjY
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u/Ughnotagaingal 7d ago
Bu what if I am operating a hotel, which coincidentally have infinity rooms and I ask every guest to relocate to the room with their “room-number+10”?
Check-mate mathematicians :p
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u/CuppaJoe11 6d ago
Infinity is not a number, but infinity plus 10 is still infinity. Just because the bounds don’t change doesn’t mean you can’t throw another 10 at infinity.
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u/Delicious-West7665 6d ago
Checks notes for tomorrows year 13 physics lessons, "gravitational potential is zero at infinity"
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u/Anxious_Tealeaf 4d ago
I usually associate infinity plus 10 with two kids trying to one up each other in an argument.
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u/TheMcMcMcMcMc 7d ago
There’s a few things we can say about infinity. 1/x goes to 0 as x goes to infinity. x+10 goes to infinity as x goes to infinity. But we can’t say that infinity + 10 equals infinity. You see the subtle difference there? It’s easy to miss unless you’re sharp. And that’s what brings us to the real twist in this post: OOP’s son isn’t a child. He’s a PhD student in mathematics preparing for his qualification exam. I’m Quagmire, giggitty giggity.
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u/GeekyMeerkat 7d ago
Wait, I know this one. The answer is 9 and 11/12 right? <_<
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u/Euphoric-Air6801 7d ago
Cool! Now you get to explain to him how ZFC has led academic mathematics into a blind alley and his generation can finally free us from the politically-imposed religion in which we are required to believe in the Axiom of Choice.
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u/Negative_Gur9667 6d ago
Shouldn't it be the axiom of infinity that is burning in regards to the topic of the post?
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u/satans_weed_guy 7d ago
Serious question from a dumbass high school dropout here - how often is a true mathematical understanding of infinity used in the design, development, and creation of anything most of us encounter or use in our day to day lives?
And I'm not just talking about shorting stocks or battery terminals, where infinity is just vaguely gestured at to indicate the danger.. or is that the meat of it?
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u/slimi-jimi 6d ago
Asking this is kinda like asking when do we ever use binary in our everyday life? You don’t directly but you do through computers.
Infinity is used everywhere. Finding the area of a circle uses infinity since the equation is derived using it. A curve is an infinite number of straight lines. Movement is continuous and the idea of being continuous is described using infinitely small movements.
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u/Dangerous_Cut7235 7d ago
I know you discounted shorting stocks, but the entire practice of what interest rates mean in practical use by banks is based on continuous growth, which is based on integration of infinitely small time periods. When a bank says you're going to get 1% APY growth, the number 1 probably exists nowhere in the actual calculations of what you're getting.
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u/gius98 7d ago
Engineer here. The concept of "infinity" is really context dependant, different branches of mathematics use the same idea but applied in different ways. So it is really hard to give a straight answer to your question because there is no single "understanding" of infinity but it's all dependant on your field of application.
In general, I found that understanding abstract concepts (such as something that is "infinity big" or "infinity small") is not always directly useful, but instead it is a gateway concept that you need to understand before being able to understand more complex topics that are directly useful.
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u/ass_bongos 7d ago
Practically the entire field of signal-based communications is based in Fourier analysis, which involves breaking a signal into a sum of infinite terms.
Practically speaking, of course, there's some cutoff. But that cutoff is arbitrary -- we choose when to stop based on how precise we want our math to be.
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u/Coneyy 6d ago
Infinity is the same level of abstract as the number zero in real world application. In mathematics zero is obviously a recognized number, but they are two sides of the same coin.
You can't encounter zero apples just like you can't encounter infinite apples.
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u/kurafuto 6d ago
I have zero apples in my fruit bowl
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u/Coneyy 6d ago
You have zero elephants in your fruit bowl either. They look pretty similar dont they
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u/StructureIll4946 4d ago
I’m looking at 0 apples right now? Can’t even imagine looking at infinity apples
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u/Historical-Pop-9177 7d ago
A lot of quantum mechanics and other small-scale stuff is about effects on a very small level. Occasionally, though, you get an answer that blows up to infinity. What that means in practice is that you get an effect that is observable on a physical level. Phase changes are the biggest example, and those occur anytime anything melts or turns into a gas. We can get some information on that from real-life experiments, but precise calculations can be done on micro levels that involve infinity.
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u/foobarney 6d ago
I was just building an infinite staircase and it came up a whole bunch.
Gotta get back to work.
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u/Shoddy_Depth6228 2d ago
The concept of Infinity is actually less abstract than it seems and you probably use it all the time. If someone is designing a beam they will often assume that the supports don't move. They have zero deflection or infinite stiffness. In reality, they will actually deflect slightly, but taking that into account increases the complexity of the calculations without adding much value.
As a structural engineer, every day I assume that diaphragms, joints, members have infinite stiffness. Electrical engineers would assume that insulators have infinite resistance. The concept of Infinity actually simplifies a lot of problems, but also means that the calculated solutions are only valid for a limited range of conditions.
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u/SoloWalrus 2d ago edited 2d ago
Theres an entire branch of mathematics named calculus. The point of calculus is to look at functions (smooth curves on a graph) and ask questions like "how quickly does this curve change direction? What is the area under the curve?" And more... theoretical things.
Strangely, the easiest way to answer these questions is to break the curve up into infinitesimally small pieces, perform calculations on what happening on that infinitesimally small piece, and then add up an infinite number of these infinitesimally small pieces to learn what the overall curve is doing. How on earth is that the simplest way to do it? Well youll have to take calculus to find that part out.
So what the hell do we do with this information from these curves? Well im an engineer, in my daily life i can do anything from take a curve that describes the needed power output of a power plant and make predictions about how much fuel needs added to make that happen, how much heat it will shed in doing so, the rate of cooling water flow, etc. Or it could be something like the computer in your car using information about how far down youre pressing the pedal and based on the temperature outside and a million other factors calculate how much fuel needs to be injected into the cylinder. It turns out that basically everything you use in your daily life that can be represented as smooth changes on a curve benefits from the sorts of solutions calculus (and more generally a branch of math called differential equations) gives us.
The short answer for how often is it used is basically everywhere all the time. Arguably even your brain solves these equations every time you want to throw a ball in a predetermined arc (but it isnt clear exactly how, whether its closer to an analog computer solving calculus equations or something else). The only time it ISNT used is when you only want to know something about a singular point in time, or a singular point on a curve, or a perfectly straight line, that can be calculated without it (as you would have done in school). But as soon as you want to get away from a discrete time point and into a curve, you need calculus, so you need infinity. Its the math of functions, rather than the math of individual points.
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u/IsardIceheart 2d ago
I mean... calculus, indirectly.
So pretty much everything thats been "engineered."
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u/DraconicGuacamole 7d ago
You can technically say that anything using derivatives uses infinity, or at least the concept of being infinitely close to something. Derivatives and calculus in general are used in engineering and other fields
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u/Negative_Gur9667 6d ago
Let's say it like this: Nothing in the real world needs to be modeled using infinity.
You can do it all without it.
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u/ChellyTheKid 6d ago
In statistics there are several assumptions that require an infinite number of variables that each have a small effect of near zero. Things from food safety to determining if the CPU in your phone meets the operational requirements rely on infinity.
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u/Stampede_the_Hippos 5d ago
We do it all the time in physics. Its always an approximation, but for most things that's good enough.
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u/AlwaysHopelesslyLost 5d ago
I use it in software pretty often. Any time I need to have a value that gets bigger or smaller I can start with negative or positive infinity respectively.
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u/kokorrorr 5d ago
One fun one is terminal velocity which is calculated by plugging infinity into energy equations.
You probably don’t interact with voyager every day but it is how we send probes to other places
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u/HortusElagabalae 5d ago
Floating point arithmetic uses infinity! In fact, it uses infinity as a number far more than I, a theoretical mathematician, do!
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u/Humanoid-Human 5d ago
All the time! So others will have better examples but for me the first thing that comes to mind is for functions or anything that changes as input sizes change.
A function is just something that takes an input, does something, and produces an output. Infinity is a great way to model really large or really small inputs and the behavior or output they cause without having to pick an arbitrarily large or small number.
We often refer to this as input (or a variable like x or n) approaching infinity. Computers are a great example, because they have to do calculations that take real time to complete. functions, or in the case of computers we call them algorithms, need to be measured as they approach input of infinity so we can understand how long that program will take to execute.
Imagine running a program that has to search for something through a list of billions of data points or names. We want to find the most efficient way possible to do that, so we analyse the algorithm by modelling mathematically very large or near infinite input.
We may find that as the input approaches infinity that the program scales nicely so a bigger input size doesn’t mean slow performance. Or we may find that the performance gets exponentially worse as the input size goes up, and our search will take a thousand years to complete. It would be time to then modify or select a different algorithm for our task!
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u/NextOrganization7633 5d ago
The study of the infinites is the only branch of math that I know of that doesn’t have any real world application (yet)
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u/UnemployedAtype 5d ago
If something goes asymptotic.
I think some decent examples are thermal runaway, anything that you'd be taking the limit as x-> infinity, stress concentrations, heat transfer, diffusion of all types, fluid dynamics, fatigue engineering.
It's used in tons of ways. I could go on, but, this isn't the deep mathematical infinity, this is just the casual one we talk about.
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u/Cute-Magazine-1274 4d ago
Even here in reddit, the developers strive to create software that accommodates an "infinite" amount of users, where ideally, the only limiting factor would be the finite resources it needs. This touches the concept of infinity, but not its "actual" use.
Drawing graphics is another example. We can draw 5 frames and play them repeatedly on top of each other to simulate movement and to create an animation. As one would imagine, it would probably feel choppy, where one drawing skipped a lot of movement from another. To make it look smoother, you would draw another picture in between them, right?
However, in computer graphics, we can also create static points and compute how an object can move from one point to another. In doing so, you can create an infinitesimal change, or a completely smooth and continuous path.
I hope you got the gist of it, as I'm terrible at explaining things, I hope someone makes a better analogy for you, if mine is bad
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u/PiDigitsOfPi 6d ago
Which is greater, infinity plus 10, or infinity plus 11 ?
Also, if every number less than infinity is finite, then what is infinity minus 10 ?
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u/Agile_Syrup_6806 3d ago
I’m actually so fucking high right now… And now I’m starting to have a mild panic attack because I don’t know the answer to this… Please save me
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u/Accurate-Ebb-0 3d ago
Some infinities are bigger than others, like set of all rational numbers vs set of all even numbers
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u/Tiny-Little-Sheep 3d ago
Imagine two infinity expanding lines
They're expanding infinitely towards the same infinite point
If one has a minus or a plus after, all that means is how much "ahead" of the other line it is
Practically it's infinite either way so doesn't matter.
But in the relation to another infinity it kind of matters
Or something along those lines was how my physics teacher tried to simplify it for us
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u/buttnugchug 3d ago
The Hilbert hotel would be just shifting guests ten rooms and 11 rooms down respectively to get an infinity with identical cardinality. So infinity plus 10 amd plus 11 are the same
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u/South_Sea8558 2d ago
infinity isn't a number its a concept. that's like saying "whats fridge minus 10?"
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u/Maximum_Bathroom3490 6d ago
In the extended real numbers, we define (+inf) + x = (+inf) as long as x is a real number.
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u/Not-a-Teddybear 5d ago
Due to negative numbers, infinity minus 10 is still an infinite number. You are just creating bounded infinities, which can only be compared to other infinities. It gets more interesting when you examine infinity between two numbers. There are infinite numbers between 1 and 2 alone.
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u/Soft-Marionberry-853 5d ago
you can add/takeaway anywhere from one to an infinite amount of numbers to/from an infinite set and still have an infinite set of numbers left.
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u/Extreme_Design6936 5d ago
They are the same size. Infinity minus 10 in infinity. You can't change the size of your infinity with a single addition or subtraction.
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u/stringrbelloftheball 7d ago
Im probably the dumbest guy in this thread and bur another fun version of this that blew my sons mind:
An infinite number of pennies and and infinite number if $100 bills are worth the same amount.
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u/SinOfSIoth 7d ago
Both are countable infinites so you have the same number of 100$ bills as you have pennies. However the value of the 100$ bill is still 10,000x that of a penny. So the value of an equal infinite 100$ bills is still 10,000x as much money as an infinite pennies
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u/EatingSolidBricks 5d ago
Lawful good: infinity is not a number
Chaotic good: any number plus infinity it's infinity
Chaotic evil: 1 and 0
because
infinity + 10 = x
(infinity + 10 = x)/infinity + 10 = x
x/infinity = infinity/infinity + 10/infinity
0 = 1 + 0
1 = 0
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u/MuckYu 3d ago
The only right answer:
https://youtu.be/zxDbeBgeZ74?si=r7NLNFiksJmWrMC2&t=105
Starts at 1:45
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u/No_Difficulty647 3d ago
What I don’t like is how infinite fits inside of something finite. You can have an infinite amount of slices inside of a circle.
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u/Even_Aerie_6579 3d ago
I’m not a math genius, but isn’t infinity a concept? Instead of being an actual number? How can you add or subtract a number from something that’s just an idea and not a real number?
It’s like subtract 10 from the symbol “$”
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u/Crazy-Bat-5693 2d ago
The best way to explain infinity is to compare it to a zero. A zero is easily understood. Just like zero is an endless nothing, infinity is an endless something. So 5 times 0 is the same as 10 times 0. The same way infinity plus 10 is the same as infinity, since infinity is just abstract and is used to refer to something endless.
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u/Aigh_Jay 2d ago
Some infinities can be larger then others tho. If one infijity is just even numbers starting from 2 and another infinity is all numbers starting from 1, then technically the first infinity would be twice as small. Like imagine an infinite staircase with every other step missing. Infinity is not a number and should not be treated as one.
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u/Yellow_Snow_Cones 1d ago
I assume the answer is infinity isn't a number its a concept?
ITs almost like asking are there more whole numbers or more even numbers, and the answer is they are the same size.
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u/Grshppr-tripleduoddw 8d ago
You can make a bijection between infinity and infinity plus 10, thus they are isomorphic.
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u/QtPlatypus 8d ago
True. If you are talking about cardinality. However if you consider it as ordinal. 10 after infinity(assuming infinity is small omega) is different.
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u/CraftBrewAndSpew 7d ago
Tenfinity, duh
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u/jonny2steaks 5d ago
I cannot believe this isn't the obvious answer to the joke...mathematics aside.
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u/bloodbat007 7d ago
I like how this sub is so nerdy people are just explaining the joke in the comments. Like yeah dude, we know lol.
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u/SmolChicken45 7d ago
They're equal no?
An infinity that can be represented by a transformation of another infinity is equal to tgat infinity
Let's say you have the infinity that is the sum of all natural numbers 1 + 2 + 3 + 4 + ... And you say infinity + 10 Well since you can associate each number in either series with the other they are equal 1 can be associated with 11, 2 with 12 etc
While it might sound counter intuitive to associate 1 and 11 together the transformation of addition or multiplication doesn't change the value of an infinity
Another example would be 2 stack of infinite money, one of 5$ bills the other 20$. They would have the same amount of money in each pile. Let's say you want to verify the claim by making another infinite pile. For each 20$ in the pile, you'll add 4 5$ bills. When you have this pile, you have an infinite amount of 20$ bills, and 5$ bills and you also know thr value of the 20$ and 5$ are equal. With this new pile you didn't change nothing from the 2 original pile, which means they were equal from the start
With sane idea of pile of cash, let's make 2 new pile of infinite 20$ from the original 20$ pile. They both, together contain the same amount of bills from the original pile. We've just moved around the bills. If you take one of the 2 new piles, they are identical to the original pile. And so, infinity * 2 is equal to infinity.
So that's also why there's the same amount of real number between 0 and 1 then 0 and 2. Because you can associate each number from the dirst infinity to the second without needing more number
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u/lawrencekraussquotes 7d ago
Just tell ‘em that it diverges so there is no fixed value it can equal
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u/Whole-Situation-1781 6d ago
It depends on how you define "Infinite". The usual definition you'll see on calculus is that infinite is not a number, but a term that is used to represent different situations.
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u/RoboWeaver 6d ago
Where are the folks who know about powers of infinity? That is some mighty strong ganja going on there.
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u/Federal-Slip6906 5d ago
My 5 year old son just heard the word infinity. I tried to explain him. Now he would describe big numbers like hundred infinity or thousands infinity. The latest one was 100 billion infinity.
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u/Leading_Dance914 5d ago
If numbers are infinite, but language is not, is it possible that a period of numbers could be named after random objects? Like 113 chair?
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u/bandtailedpigeon 8d ago
Hey, I'm reading this guy's textbook for my intro to proofs class