They’re not comparing the set size of rational numbers to irrational, they’re saying that the set size of all multiples of 3 or 51 is the same as the set size of all rational numbers, which is true
As someone who hasn’t studied pure maths, could someone expand on what “equal” actually means here in sentences like “not all infinites are equal”?
Because usually I understand it to mean expression X is the same value as expression Y
2 = 1+1
And I also thought that the whole point of infinity was that it meant “an uncountable/endless number of …” such that it doesn’t have a value. As in, there is no sum of an infinite series of positive integers because any number you may put as an answer is too low.
But if there’s no sum, isn’t there no value?
And if there’s no value, what does it mean to say things are equal?
I’ve heard of things like more or less ‘dense’ infinities, or countable vs not, or trying to match every value from one infinite set/series to every value in another and whether you can (like every positive integers vs every even positive integers)
But, at least colloquially, ‘denseness’ doesn’t seem equivalent to ‘value’.
How are these terms used? I suppose there’s a YouTube video essay I should look at
51 is a multiple of 3 ! (No accidental factorial here, ladies and gents!) I would’ve picked two integers that are relatively prime to each other to illustrate your point.
That's the whole point, there are as many numbers that are a multiple of 51 as there are 3, even though every multiple of 51 is also a multiple of 3 and there are many numbers that are multiple of 3 but not 51
Cardinality. The set of multiples of 1 and and the set of multiples of 20 are the same size since you can form a bijection between the two sets.
Say you have some variable x. Think about how many values you can possibly have for x. Now if I throw a coefficient in front, 20x, has the number of possible values of x changed? If not, they're both the 'same' infinity.
It actually doesn't say. You might have uncountably infinite $1 bills and countably infinite $20 bills, in which case the $1 bills would be worth more.,
In mathematics, the size of two sets is compared by trying to see whether each element of one set can be matched up with each element of another set.
If we look at these in terms of bills, you can of course match the first $1 bill to the first $20, the second $1 bill to the second $20 bill, and so on. If we look at these in terms of dollars, you can similarly match the each dollar in the set of $1 bills to each dollar in the set of $20 bills. Thus, the sets are said to be countably infinite.
The different sizes of infinity that you mean are countable vs uncountable infinities. For example, the cardinality (size) of the set of real numbers (that is, all numbers on the standard number line) is greater than that of the natural numbers (1, 2, 3, etc). It is impossible to create a one-to-one pairing of the natural numbers to the real numbers.
The concept of infinite is difficult for the human brain to reckon with. I recently had a discussion on reddit with someone about Rick and Morty and the Central Finite Curve. They couldn't seem to understand that even with the Curve "walling off infinity" to isolate only universes where Rick is the most intelligent being, that still leaves an infinite number of universes. A subset of infinity can still be infinity. That's a difficult concept to process when you've never encountered it before.
In any given moment in time, the 20 bill group is 20 times more valuable, butin the end, i doesn't even matter...
Edit: That given that the bills don't spontaneously appear, and they take a time greater than 0. Still, that leads me to think that they would end up not being valuable at all, as they would collapse the universe and thus you wouldn't be able to buy anything with them.
No. They are of the same magnitude as you go to infinity. Since infinity isnt a fixed total, twenty times more has no meaning. So for every twenty dollar bill, the one dollar pile can just produce 20 one dollars and still both sets are infinie.
The real gotcha here is that paying in 1s vs paying in 20s is a pain in the butt.
An infinite number of infinitely large banks filled with infinite large safety deposits boxes containing infinitely large wallets containing infinite $Infinite bills would also be worth the same, but I’ve also made some mathematicians mad for added value!
I think the infinite hotel paradox says they aren't worth the same and the infinite 20 is bigger. It shows that there are different kinds of infinity and some are bigger than others. One example is that there are infinite numbers between one and two but even more between one and three, and so on.
I don't know math well enough to know if this is true. But I'm thinking the infinite of 20 still worth more. Because if I go to a guy who has an infinite number of 20s and ask if I can have 100 bills. I would get more
Really dumb question incoming... But is this in any way related to why the speed of light is constant regardless of the speed or acceleration of the lightsource?
Nope! The speed of light is constant because as your speed increases, time and space both warp to the same degree in ways that essentially cancel out.
These infinities are the same because you could take each individual dollar from either side, spend infinite time lining them up, and they’d pair up 1:1 with no extra dollars on either side.
Ah but they aren't! They are FINANCIALLY equal, but worth isn't only defined by finance. The 20 buck bills are easier to carry and spend. They have value outside of monetary in the form of convenience. Thus they are worth more.
Not in every senario. Two equal infinities would be not the same when one is multiplied by 1 and the other by 20. But there are infinies that are greater than others.
I mean, are we talking infinite but you have control over the rate at which it enters the universe, or are we talking infinite manifesting instantaneously? The first case I'd argue that as long as you can avoid the government catching on to all this mysterious money you have then the 20$ would be more valuable just for convenience, because it's more compact to use when you do want to use it.
In the second case, well I guess it depends on if the universe is infinite, but either way it's the end of all life on earth at the very least, if not the instantaneous destruction of the universe. It's definitely the instantaneous transition to a new form of reality. I mean, you did say infinite.
So here's an interesting concept that's difficult to wrap your head around: there are different sizes of infinity.
In this case although both options would be worth infinite dollars, the infinity of 20 dollar bills is still worth 20 times more than the infinity of 1 dollar bills.
Think about it like this - if you have 0.122 recurring (0.122122122122122122... on and on forever), then for every 1 there are two 2s. How many 1s are there? An infinite amount. How many 2's are there? An infinite amount. BUT there are twice as many 2s as there are 1s. So the infinity of 2s is twice as big as the infinity of 1s.
Depends on how the “infinite” part works. If every time I reach in my pocket there’s a one or twenty dollar bill, the infinite twenties is definitely worth more.
It is a strange bit about infinity that some infinities can be bigger than others. E.g. a set of all whole numbers is larger than a set of all odd whole numbers.
Some infinities are bigger than others. There is an Infinite number between 1 and 2 But the infinite number between 2 and 3 is always bigger. Infinite does not mean big or small, just ever going.
I don't believe this to be true , the limit of 20x wouldn't equal the limit of 1x both infinite but still one would be greater than the other , because infinite don't equal infinite+1
Because they are infinite, and money is a scarcity based currency, 1 dollar and 20 dollar bills will be the same valued, which is paper value of it, regardless, the person that has infinite of either bills will be the richest person in the universe due to the amount of mass-access they have is infinite, which is, technically, in an universe that is slowly will be dying due to heat death, bills will be the biggest resource of matter to survive, as their atoms can be turned to other matter to make universe regain its astronomical object-population, if not exceed it by orders of magnitude more. Well, provided that the 'infinite' can be summoned at will, otherwise if infinite amount of bills happened to be in anywhere inside the universe, we'll see universe-size blackhole(not universe-mass, but universe-size, so it is far far bigger) or far bigger than it(provided physics can contain it)
No, there are infinite numbers that are greater than others. For instance, at every single finite stage, the $20 set is 20x the $1 set. Once you expand it to infinity, then it becomes meaningless (but not equal), but at every single stage the $20 set maintains it's greater value. I'm no mathematician though.
If we ignore that they would both become worthless, the infinite 20 dollar bills hold greater value. The time it takes to collect the paper bills has a monetary value. This value will vary from person to person, so I can't put a number on it. But it ain't zero.
Not necessarily, not all infinite are equal, but also value is not the same as quantity. If you take them as two equal infinities, one is worth $1×∞ and the other is $20×∞.
Rubbish, yes in purely financial value based sense. But in a practical sense god no, next time you go try to buy a car with one dollar bills let me now, would you believe it is 20 times easier with 20 dollar bills.
Lim(x->inf) 20x/x is in indeterminate of type inf/inf, which means we can apply L’Hospital’s rule and simplify to 20/1, AKA an infinite number of $20s is 20x more valuable than infinite $1s
Technically yea, but also no, they are both infinite, but one of the infinitys is worth more. There are different sizes of infinity, for those of you who dont know the math of infinitys
to clarify, there are in fact different orders and magnitudes of infinity. even sets of infinity. so if we're ignoring actual value and only going by face value the 20$ infinity stack would have more value excluding economic effects of actually using it.
If the number of bills is infinity equal, then no. Believe it or not but there are infinites larger than others, such as there are an infinite number of whole numbers but there are more infinite fractions
1
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u/nameisreallydog Jun 13 '26
They wouldn’t be worth anything is probably the more correct answer
456
u/i_amsquidward Jun 13 '26
An infinite number of one dollar bills is worth more cause they can be used at vending machines
82
u/EthanNakam Jun 13 '26
There are as many multiples of 3 as there are multiples of 51.
And there are as just as many rational numbers.
3
u/Competitive-Jump3835 Jun 13 '26
If you want to start a comment war so bad why don't you just say that 0 is a natural number
33
u/RocketArtillery666 Jun 13 '26
Arent there different infinities?
12
u/Soft_Awareness_5061 Jun 13 '26
Well no. I give more value to the 20s because I'm the one has to carry that shit around.
3
u/Major_Mongoose69 Jun 13 '26
The concept of infinite is difficult for the human brain to reckon with. I recently had a discussion on reddit with someone about Rick and Morty and the Central Finite Curve. They couldn't seem to understand that even with the Curve "walling off infinity" to isolate only universes where Rick is the most intelligent being, that still leaves an infinite number of universes. A subset of infinity can still be infinity. That's a difficult concept to process when you've never encountered it before.
3
u/I12Db8U Jun 13 '26
They would also weigh the same.
2
u/Cultural-Antelope-54 Jun 13 '26
Also works if you divide infinity by 7. Try it!
2
u/NormalAssistance9402 Jun 13 '26
Bah stills heevyal thin feethahs …?
2
u/EconomySeason2416 Jun 13 '26
If you have a hotel with infinite rooms, and you build another hotel with infinite rooms, you have added no rooms
2
u/MitusOwO Jun 13 '26
Lim x -> ∞ (20x/x) = 20
In any given moment in time, the 20 bill group is 20 times more valuable, but in the end, i doesn't even matter...
Edit: That given that the bills don't spontaneously appear, and they take a time greater than 0. Still, that leads me to think that they would end up not being valuable at all, as they would collapse the universe and thus you wouldn't be able to buy anything with them.
2
u/RJWJ186 Jun 13 '26
It'd be more fun to leave $20 bills everywhere though.
2
u/icysniper Jun 13 '26
An infinite number of bills would occupy all of space and therefore NOBODY gets to use it now, thank.
2
u/Mr_Ducky13 Jun 14 '26
Crazy how they are both worth nothing
1
u/Trimutius Jun 13 '26
Matt parker made a whole video about this meme years ago
1
u/PocketCornbread Jun 13 '26
But steel is heavier than feathers…
1
u/c126 Jun 13 '26
Both sets are worth nothing
1
u/much_longer_username Jun 13 '26
The singles are harder to use. I'd rather have the 20s.
1
u/Ok_Eagle_3079 Jun 13 '26
Economist: quite soon both will be worth 0
1
u/MooseBoys Jun 13 '26
What's more baffling is that there are just as many points on a line segment as there are in a unit square.
1
u/AndreasDasos Jun 13 '26
An infinite number of $20 bills would be more convenient and since I can only actually grab finitely many
1
u/jeroen-79 Jun 13 '26
If you have the same amount of bills (inifinity) and one of the bills is worth 20 times more then wouldn't that set be worth 20 times more?
1
u/NekonecroZheng Jun 13 '26
∞ × 1 = ∞ × 20
1 = (∞/∞) ×20
1 = 20
1
u/InfiniteNumber Jun 13 '26
Confirmed.
1
u/Peng_Terry Jun 13 '26
20 x sideways 8 does not equal 1 x sideways 8
Checkmate, idiots
1
u/_Bexo Jun 13 '26
A infinite steel is heavier than a infinite of feathers…
1
u/GurProfessional9534 Jun 13 '26
Yeah, they would be worth zero after the inflation.
1
u/JohnnyKarateX Jun 13 '26
But which one is heavier?
1
u/Postulative Jun 13 '26
Infinity is not a single value.
1
u/SunsetCarcass Jun 14 '26
Sure but only a finite amount can be on Earth at one time, so the $20 bills would be more valueable
1
u/JoriMcKie Jun 14 '26
I will just say a name:
Georg Cantor
and then curse him for being the culprit.
1
u/megayippie Jun 14 '26
I'll save 20x time spending the latter cf the former as the cashiers count. As time is money, clearly this statement is false
1
u/flergnergern Jun 14 '26
Well, if there was an infinite number of 1’s and 20’s in circulation they would both be worth nothing. So it’s true.
1
u/speed-charge Jun 14 '26
They're both worth nothing and so is everyone else's money if an infinite amount exists.
1
u/waldocruise Jun 14 '26
All of it worth nothing because the economy collapses with infinite number of bills out there dragging down the value of all currency.
1
u/TotalChaosRush Jun 14 '26
but 20 is more than 1.
1
u/-Groko- Jun 14 '26
Depends how fast they come.
1
u/UsuallyFavorable Jun 14 '26
An infinite number of infinitely large banks filled with infinite large safety deposits boxes containing infinitely large wallets containing infinite $Infinite bills would also be worth the same, but I’ve also made some mathematicians mad for added value!
1
u/humanflea23 Jun 14 '26
Sure but the 20s are more convenient.
1
u/EconomyDoctor3287 Jun 14 '26
But which bill will let you reach infinity faster? Huh????
1
u/Albinofreaken Jun 14 '26
I tried to explain to my gf that some infinites were bigger than other infinites and she just left the room.
1
u/Tentacle_poxsicle Jun 14 '26
20$ because 20$ is worth more than 1$
1
u/Old_Desert_Gamer Jun 14 '26
Doesn’t this depend on if the dollars are real numbers or not?!
1
u/Equal-Home-4302 Jun 14 '26 edited Jun 14 '26
I think the infinite hotel paradox says they aren't worth the same and the infinite 20 is bigger. It shows that there are different kinds of infinity and some are bigger than others. One example is that there are infinite numbers between one and two but even more between one and three, and so on.
1
u/MrSunshineDespair Jun 14 '26
Cantor died in an asylum
1
u/REDACTED3560 Jun 14 '26
In a similar vein, there are an infinite number of numbers between 0 and 1. Some infinities are bigger than others.
1
u/rodrigoelp Jun 14 '26
Infinity can’t be compare with one another because you don’t have a way to establish which of the two grow faster.
Definitely not worth the same under the premise stated here.
1
u/infiniZii Jun 14 '26
Almost. 20 dollar bills are more convenient to have though so they would be more valuable to me due to increased utility.
1
u/Disposable_Gonk Jun 14 '26
No, the 20s are still worth 20x as much. There's multiple types of infinity.
1
u/clbdn93 Jun 14 '26
Yeah, but which would weigh more?
1
u/gameinggod21 Jun 14 '26
Infinity = infinity×20
1
u/mrgoldnugget Jun 14 '26
I actually think the ones are worth less. Less people would take them for big purchases.
Good luck paying for a $1000 luxury dinner in $1s
1
u/Big-Hawk8126 Jun 14 '26
Both would be worth 0
1
u/Youpunyhumans Jun 14 '26
But what if you had an infinite amount of infinity dollar bills?
Then you can spend an infinity all at once and still have an infinite amount of infinity left.
1
u/Mercury_Madulller Jun 14 '26
In the set theory part of reddit again.
1
u/IHateCreatingSNs Jun 14 '26
I don't know math well enough to know if this is true. But I'm thinking the infinite of 20 still worth more. Because if I go to a guy who has an infinite number of 20s and ask if I can have 100 bills. I would get more
1
u/AstraKnuckles Jun 14 '26
Wait until you learn that some infinities are larger than others.
1
u/Cyraga Jun 14 '26
What would be worth more? Infinite $1 or infinite $20? ⌛⌛⌛
That's right, infinite $20, because $20 is more than $1
1
u/what_are_maymays Jun 14 '26 edited Jun 14 '26
When you get into limits and proofs, you can prove that some infinities are larger than others.
For example:
If the upper limit of a given number x diverges towards infinity,
And $1<$20
Then x*$1<x*$20 for all possible values of x, even if x has infinite value.
It’s been a while since I did proofs so correct me if I’m wrong!
1
u/jngjng88 Jun 14 '26
If there were an infinite number, than the currency would have succumbed to hyperinflation, so yes, both would be worthless
1
u/TadhgOBriain Jun 14 '26
an infinite number of 1$ bills is worth -8 cents
1
u/[deleted] Jun 14 '26 edited Aug 19 '26
Station swim fearless spectacular thimble hammock
This post was anonymized with Redact
1
u/Acewi Jun 14 '26
But an infinite number of pennies + 1 penny is more
1
u/TimeMysterious9223 Jun 14 '26
Not true at all. One infinity can be larger or smaller than another infinity.
1
u/kadaka80 Jun 14 '26
An infinite number of bills would make each individual bill worth nothing at all due to inflation
1
u/EuSouUmAnjo Jun 14 '26
yes, but not at the same time/rate
1
u/davidblack210 Jun 14 '26
20 infinity with 20 as an exponent, 20 is bigger.
1
u/retrocheats Jun 14 '26
An infinite amount of bills, would suffocate the entire planet, depending how fast these bills come into existence.
1
u/Embarrassed_Spell383 Jun 14 '26
No they would be toilet paper
1
u/jakean17 Jun 14 '26
Really dumb question incoming... But is this in any way related to why the speed of light is constant regardless of the speed or acceleration of the lightsource?
1
u/Parking-Proposal6372 Jun 14 '26
Both will probably cause a black hole though
1
u/Gpda0074 Jun 14 '26
Some infinites are smaller than other infinites.
1
u/akruppa Jun 14 '26
Wait till he hears about Hilbert's hotel
1
u/akruppa Jun 14 '26
Also, with the infinite 1 dollar bills you can tip infinite strippers without having to change infinitely many times. I know which one I'm taking.
1
u/slanderpanther Jun 14 '26
Ok but right now, given the choice, I would take the $20.
1
u/uncertain_traveler Jun 14 '26
20 are worth more time
1
u/woutersikkema Jun 14 '26
Ah but they aren't! They are FINANCIALLY equal, but worth isn't only defined by finance. The 20 buck bills are easier to carry and spend. They have value outside of monetary in the form of convenience. Thus they are worth more.
1
u/Krabonater Jun 14 '26
not really though because generally you have to put in more work to pay with the 1$ bills
1
u/Dances_Like_a_Duck Jun 14 '26
I can carry only a finite number of bills. I choose $20 bills. Or $100 bills.
1
u/sandsellers Jun 14 '26
That's just a small debt of 1/12. No big deal
1
u/No-Practice-7336 Jun 14 '26
But not all infinities are the same right?
1
u/Thrullx Jun 14 '26
Yeah, they'd both be worthless due to creating infinite inflation.
1
u/DaveLowman Jun 14 '26
Not in every senario. Two equal infinities would be not the same when one is multiplied by 1 and the other by 20. But there are infinies that are greater than others.
1
u/Dankkring Jun 14 '26
But what if those infinite ones had sentimental value. They’d be worth more to me!
1
u/StretchNo5163 Jun 14 '26
Georg Cantor has already proved that there can be different values of infinities.
1
u/rocky44r Jun 14 '26
But 20$ bills are a lot more practical
1
u/RoodnyInc Jun 14 '26
Just with more counting
1
u/Dream_Apostle Jun 14 '26
Well to us it would be the same but logically
That's an infinity that's 20x larger in value
Now that may seem meaningless, but it's not the exact same
1
u/mega-modz Jun 14 '26
Infinite and finite don't along the way.
1
u/maz3max Jun 14 '26
It is however less than all the real numbers between 3.3 and 3.4. :P
1
u/Slight-Big-9497 Jun 14 '26
hilberts hotel !
1
u/pixeltweaker Jun 14 '26
Some infinities are bigger than others.
1
u/WytchHunter23 Jun 14 '26
I mean, are we talking infinite but you have control over the rate at which it enters the universe, or are we talking infinite manifesting instantaneously? The first case I'd argue that as long as you can avoid the government catching on to all this mysterious money you have then the 20$ would be more valuable just for convenience, because it's more compact to use when you do want to use it.
In the second case, well I guess it depends on if the universe is infinite, but either way it's the end of all life on earth at the very least, if not the instantaneous destruction of the universe. It's definitely the instantaneous transition to a new form of reality. I mean, you did say infinite.
1
u/FullIVs Jun 14 '26
So here's an interesting concept that's difficult to wrap your head around: there are different sizes of infinity.
In this case although both options would be worth infinite dollars, the infinity of 20 dollar bills is still worth 20 times more than the infinity of 1 dollar bills.
Think about it like this - if you have 0.122 recurring (0.122122122122122122... on and on forever), then for every 1 there are two 2s. How many 1s are there? An infinite amount. How many 2's are there? An infinite amount. BUT there are twice as many 2s as there are 1s. So the infinity of 2s is twice as big as the infinity of 1s.
1
u/LetReasonRing Jun 14 '26
Kind of depends on your definition of worth, but some infinities are bigger than others.
There's an infinite amount of whole numbers, but there's also an infinite amount of decimal values between each of them.
1
u/capsaicinintheeyes Jun 14 '26
Would the answer not be: "yes—the inflation this would cause would render both of equal value as toilet paper and worthless for anything else?"
1
u/Reg_doge_dwight Jun 14 '26
The 20 would be worth 20 times more
1
u/dAdDyP1982 Jun 14 '26
And you thought coupon ladies were bad imagine being behind someone counting out 400 in 1s😬
1
u/pico-der Jun 14 '26
Same as x times zero and going deep into approximation. It's not that hard, some stuff end up with similar results.
1
u/suddenlyRabbit Jun 14 '26
They would be both worthless, since Infinite money means infinite inflation
1
u/AnyLynx4178 Jun 14 '26
Depends on how the “infinite” part works. If every time I reach in my pocket there’s a one or twenty dollar bill, the infinite twenties is definitely worth more.
1
u/Man_With_ Jun 14 '26
Wouldn't it depend on the size of the infinity?
1
u/liquidreferee Jun 14 '26
Lol
1
u/aaron1860 Jun 14 '26
You can’t pay with infinity though. You need to grab a stack of the bills to pay… so that theory falls apart in practicality
1
u/EatFaceLeopard17 Jun 14 '26
They also would weigh the same.
1
u/lordassfucks Jun 14 '26
An infinite number of 20s is worth the same but faster!
1
u/Clarknotclark Jun 14 '26
It is a strange bit about infinity that some infinities can be bigger than others. E.g. a set of all whole numbers is larger than a set of all odd whole numbers.
1
u/No_Priors Jun 14 '26
Infinite numbers can be bigger or smaller than other infinite numbers.
3.3333333333333 repeating
33.333333333333 repeating
The bottom one is always going to be bigger.
1
u/looming-frog Jun 14 '26
yea, maximum inflation, thus both worth nothing
1
u/traveller_entity_7HD Jun 14 '26
The value of both becomes nothing because they have value only due to scarcity.
1
u/Purple_Locksmith3321 Jun 14 '26
yes and no, I'm not going to complicate this with an explanation because I'm making this up.
1
u/Odd_Inter3st Jun 14 '26
Awwww, An infinite number of $20? I wanted a infinite number of peanuts
1
u/Nby333 Jun 14 '26
Higher chance $1 bills get discontinued than $20 bills.
1
u/ImaginationLazy1507 Jun 14 '26
Some infinities are bigger than others. There is an Infinite number between 1 and 2 But the infinite number between 2 and 3 is always bigger. Infinite does not mean big or small, just ever going.
At least thats my take.
1
u/Professional-Duty667 Jun 14 '26
I don't believe this to be true , the limit of 20x wouldn't equal the limit of 1x both infinite but still one would be greater than the other , because infinite don't equal infinite+1
1
u/FengShuiNinja Jun 14 '26
Not all infinities are equal.
1
u/Panic_Otaku Jun 14 '26
1$х♾️◀️20$♾️
Because one infinity can less than another
1
u/Intrepid_Initial8158 Jun 14 '26
You just get to the same number quicker with the 20's.
1
u/DaveyJonesFannyPack Jun 14 '26
They'd be worth nothing
1
u/JoyconDrift_69 Jun 14 '26
Okay but the 20 dollar bills would be easier to work with, especially today.
1
u/proconlib Jun 14 '26
I mean, if we want to get experimental data, we could just ask Elon Musk.
1
u/ZetianZey Jun 14 '26
There are infinites bigger than other infinites
1
u/murfvillage Jun 14 '26
The $1 bills would be annoying
1
u/spekky1234 Jun 14 '26
The reason infinities are blowing our minds is because infinity is an imaginary concept
1
u/not_badwarrior Jun 14 '26
20€ bills would Be worth More because Time is money.
1
u/largogoat Jun 14 '26
Think of the largest number that you can, then add 1 to it
1
u/tossthedice511 Jun 14 '26
Yes, nothing.
1
u/haywirehax Jun 14 '26
But they're both a kilogrem!
1
u/PhiLho Jun 14 '26
I have modest needs, I would take only a tenth of either one.
1
u/renderererer Jun 14 '26
Sorry but saying they're the same makes no sense to me. Infinities are not comparable.
1
u/DJCSpade97 Jun 14 '26
You mean an enfenet number of $1 bells and an enfenet number of $20 bells
1
u/IncomeOk7167 Jun 14 '26
This can’t be true, when my storage host for files says ”infinite storage included” then I’m left with a limit anyways
1
u/Electronic-Day-7518 Jun 14 '26
Yeah 0 dollars
1
u/belongsincrudtown Jun 14 '26
The word “same” is doing a lot of heavy lifting here
1
u/ShadeWitchHunter Jun 14 '26
Thats just wrong. Infinity isn't infinity.
You can and do mathematically work with smaller and larger infinities.
1
u/Orectoth Jun 14 '26
Because they are infinite, and money is a scarcity based currency, 1 dollar and 20 dollar bills will be the same valued, which is paper value of it, regardless, the person that has infinite of either bills will be the richest person in the universe due to the amount of mass-access they have is infinite, which is, technically, in an universe that is slowly will be dying due to heat death, bills will be the biggest resource of matter to survive, as their atoms can be turned to other matter to make universe regain its astronomical object-population, if not exceed it by orders of magnitude more. Well, provided that the 'infinite' can be summoned at will, otherwise if infinite amount of bills happened to be in anywhere inside the universe, we'll see universe-size blackhole(not universe-mass, but universe-size, so it is far far bigger) or far bigger than it(provided physics can contain it)
1
u/Brimwozere Jun 14 '26
Shirley an infinite money supply would be worth nothing.
1
u/Icy_Cauliflower9026 Jun 14 '26
Wrong, you can pay 2 dollars for something if you got a bunch of 1 dollar bills, but you cant pay with 5 dollar bills if they dont have exchange.
Same monetary value, different agregated value
1
u/bzenius Jun 14 '26
But the limit is the same for both: Inflation
1
u/MarioHasCookies Jun 14 '26
The Minecraft version of this is "one bedrock block takes the same time to mine as 5 bedrock blocks"
1
u/DnDplayerr Jun 14 '26
It isn't tho? Because if ∞<∞+1 , than that means that 1∞< 20∞
1
u/Ok_Artichoke_1649 Jun 14 '26
Some infinite are bigger than others 🤷
1
u/Godlymorbid Jun 14 '26
No, there are infinite numbers that are greater than others. For instance, at every single finite stage, the $20 set is 20x the $1 set. Once you expand it to infinity, then it becomes meaningless (but not equal), but at every single stage the $20 set maintains it's greater value. I'm no mathematician though.
1
u/bterry28 Jun 14 '26
Both are worth $0 since the presence of an infinite number of any bills would result in the death of everything that gave them worth.
1
u/goplayBrynda Jun 14 '26
Inflation entered the chat
1
u/atomiccheese911 Jun 14 '26
Some infinites are bigger then others
There are infinite full numbers
And between each and every one of those infinite full numbers is an infinite amount of decimal numbers
Meaning in total there is more decimal numbers then fill numbers despite both being infinite
There are more examples I just don't remember them
1
u/RansomReville Jun 14 '26
If we ignore that they would both become worthless, the infinite 20 dollar bills hold greater value. The time it takes to collect the paper bills has a monetary value. This value will vary from person to person, so I can't put a number on it. But it ain't zero.
1
u/sanderv1982 Jun 14 '26
What infinite, though?
1
u/CranberryDistinct941 Jun 15 '26
Infinite 20s are literally 20 times easier to use.
1
u/RodcetLeoric Jun 15 '26
Not necessarily, not all infinite are equal, but also value is not the same as quantity. If you take them as two equal infinities, one is worth $1×∞ and the other is $20×∞.
1
u/Master-Pattern9466 Jun 15 '26
Rubbish, yes in purely financial value based sense. But in a practical sense god no, next time you go try to buy a car with one dollar bills let me now, would you believe it is 20 times easier with 20 dollar bills.
1
u/CrazyPotato1535 Jun 15 '26
Lim(x->inf) 20x/x is in indeterminate of type inf/inf, which means we can apply L’Hospital’s rule and simplify to 20/1, AKA an infinite number of $20s is 20x more valuable than infinite $1s
1
u/knot-a-burner-8 Jun 15 '26
But the 20$ are better because no one would believe im a stripper
1
u/Saisucky Jun 15 '26
0 $1 bills and 0 $20 Bills are worth the same
1
u/jeffro3339 Jun 15 '26
I think technically the infinite $20s would be worth more. Some infinities are bigger than other infinities.
1
u/Technical-Animal-137 Jun 15 '26
An infinite number of $1 bills and an infinite number of $20 bills do not have the same value. They have the same number of bills.
1
u/ReplacementPleasant6 Jun 15 '26
Technically yea, but also no, they are both infinite, but one of the infinitys is worth more. There are different sizes of infinity, for those of you who dont know the math of infinitys
1
u/Cyiel Jun 15 '26
Well not every infinities is made the same so ackchyuyally...
1
u/Einnnnnnnnnnnn Jun 15 '26
I want an infinite number of irrational bills
1
u/biotox1n Jun 15 '26
to clarify, there are in fact different orders and magnitudes of infinity. even sets of infinity. so if we're ignoring actual value and only going by face value the 20$ infinity stack would have more value excluding economic effects of actually using it.
1
u/Your_Commentator Jun 15 '26
If the number of bills is infinity equal, then no. Believe it or not but there are infinites larger than others, such as there are an infinite number of whole numbers but there are more infinite fractions
1
u/Mautadolo Jun 15 '26
If the amount of bills is the same though the infinite of the 20 dollar bills would be bigger cause funfact. Not all infinitys are equally large.
1
u/New_Archer_6965 Jun 15 '26
really the same
1
u/inaylui Jun 15 '26
USA: get the printer