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plus.maths.org/content/infinityorjust112
If you're talking about the Riemann Zeta function (Z(x)), you're still wrong. For all values of x > 1, Z(x) yields the sum of all numbers (S). For all values of x < 1, the function yields finite numbers. The misconception of S = 1/12 comes from the misconception that S = Z(x) for all values of x, not just those greater than 1. Plugging in Z(1) yields 1/12, which does not = S.
The article explains that the physics actually has nothing to do with the math. It's entirely coincidental, and a quirk of the pretty much universallyagreedtobeinsane quantum physics, that the Riemann Zeta function works. If that were a reliable model for every similar situation, that would be suggesting there could exist an infinite energy density, which for obvious reasons can't happen.
Again, you're applying logic to infinity. Logic is science; infinity is mathematics. And never the twain shall meet.
You're trying to apply the rules of finite, physical objects to infinity. Whatever "this" is, you're right in that it doesn't work for every infinity because it doesn't work for any infinity. If it did, it wouldn't be an infinity.
plus.maths.org/content/infinityorjust112
If you're talking about the Riemann Zeta function (Z(x)), you're still wrong. For all values of x > 1, Z(x) yields the sum of all numbers (S). For all values of x < 1, the function yields finite numbers. The misconception of S = 1/12 comes from the misconception that S = Z(x) for all values of x, not just those greater than 1. Plugging in Z(1) yields 1/12, which does not = S.
The article explains that the physics actually has nothing to do with the math. It's entirely coincidental, and a quirk of the pretty much universallyagreedtobeinsane quantum physics, that the Riemann Zeta function works. If that were a reliable model for every similar situation, that would be suggesting there could exist an infinite energy density, which for obvious reasons can't happen.
Again, you're applying logic to infinity. Logic is science; infinity is mathematics. And never the twain shall meet.
S1 = 0 + 1 + 0 + 1 + 0 + ...
If I just rearrange "all" the zero's up front:
S1 = 0 + 0 + 0 + 0 + ... = 0
But If I rearrange all the 1's up front:
S1 = 1 + 1 + 1 + 1 + 1 + ... which is a divergent series.
And we can play other games:
S1 = 1 + 0 + 0 + 0 + 0 +... = 1
The video you posted are comparing the difference between listable and unlistable infinities, and that they are indeed different.
Given an infinite amount of discrete things, like object, like bills, they would both be listable. Meaning that they are the same kind of infinity.
And if you bothered watching the video you linked, you would see, going back to my original proof, i were comparing two listable infinities, and showing that they are the same, wher you argued that two listable infinities were not the same, which is demonstrably false.
1, 2, 3, 4, 5,...
Where each number refers to a particular dollar, and I compare to someone who has $2 for each of the $1 above which I'll write like this:
1, 1, 2, 2, 3, 3, 4, 4, 5, 5,...
Both of these sets of numbers have the same cardinality which I think you agree with. Though when it comes to the sums of each of those series I think we have come to the conclusion that it depends on who you ask. But when speaking solely about "countable" you can mess with it a bit and as long as it's still countable the cardinality will be the same as any other countable set.
so its again s2=s1+s1 =2*s1
Most comments on my post tent to break the rules of the post .
1s and 20s are objects and you have to work with that , and you change them to numbers and remove rules and limitations and get a bunch of nonesence .
The thing with this problem is that IF i could be able to answer this question/ponder for everyone and them not having a way to question it i would probably be in MIT or at least be up for Math Nobel or something .
S1 = 0 + 1 + 0 + 1 + 0 + ...
If I just rearrange "all" the zero's up front:
S1 = 0 + 0 + 0 + 0 + ... = 0
But If I rearrange all the 1's up front:
S1 = 1 + 1 + 1 + 1 + 1 + ... which is a divergent series.
And we can play other games:
S1 = 1 + 0 + 0 + 0 + 0 +... = 1
You HAVE to have the same cardinality and dont mess with it because you change the rules of mesurement . What you did was change the cardinality/growth for 1s and to get the same result as the 20s but if you did that for the 20s aswell then it would beat out the 1s again .
1, 2, 3, 4, 5,...
Where each number refers to a particular dollar, and I compare to someone who has $2 for each of the $1 above which I'll write like this:
1, 1, 2, 2, 3, 3, 4, 4, 5, 5,...
Both of these sets of numbers have the same cardinality which I think you agree with. Though when it comes to the sums of each of those series I think we have come to the conclusion that it depends on who you ask. But when speaking solely about "countable" you can mess with it a bit and as long as it's still countable the cardinality will be the same as any other countable set.
so its again s2=s1+s1 =2*s1
Most comments on my post tent to break the rules of the post .
1s and 20s are objects and you have to work with that , and you change them to numbers and remove rules and limitations and get a bunch of nonesence .
The thing with this problem is that IF i could be able to answer this question/ponder for everyone and them not having a way to question it i would probably be in MIT or at least be up for Math Nobel or something .
S1 = 0 + 1 + 0 + 1 + 0 + ...
If I just rearrange "all" the zero's up front:
S1 = 0 + 0 + 0 + 0 + ... = 0
But If I rearrange all the 1's up front:
S1 = 1 + 1 + 1 + 1 + 1 + ... which is a divergent series.
And we can play other games:
S1 = 1 + 0 + 0 + 0 + 0 +... = 1
Let's take another example. Say you go to an ant hill and you compare the status of the hill after crushing one ant, then after crushing a hundred ants. There are millions of ants in the colony; do you think your actions have affected the colony in any way? Even at only very large numbers, small numbers become completely irrelevant. When talking about infinites, still talking about small numbers like "10" and "1000" is asinine.
www.youtube.com/watch?v=SrU9YDoXE88 : A video that explains the concept of, for example, the set of all natural numbers and the set of all fractions being equal, even though fractions are provably more numerous than naturals.
The concept here is not of ALL infinities but this particular one with 1s and 20s , physical objects , object a and b with b being 20 times as valuable/big than a .
I was realy trying to make it as simple as possible .
And as you said INFINITY is not a number , and there are different kinds , but THIS particular one is just the sum of the bills .This doesnt work for every infinity , just THIS ONE because thats the rules and it makes logical sence in real world .
You're trying to apply the rules of finite, physical objects to infinity. Whatever "this" is, you're right in that it doesn't work for every infinity because it doesn't work for any infinity. If it did, it wouldn't be an infinity.
plus.maths.org/content/infinityorjust112
If you're talking about the Riemann Zeta function (Z(x)), you're still wrong. For all values of x > 1, Z(x) yields the sum of all numbers (S). For all values of x < 1, the function yields finite numbers. The misconception of S = 1/12 comes from the misconception that S = Z(x) for all values of x, not just those greater than 1. Plugging in Z(1) yields 1/12, which does not = S.
The article explains that the physics actually has nothing to do with the math. It's entirely coincidental, and a quirk of the pretty much universallyagreedtobeinsane quantum physics, that the Riemann Zeta function works. If that were a reliable model for every similar situation, that would be suggesting there could exist an infinite energy density, which for obvious reasons can't happen.
Again, you're applying logic to infinity. Logic is science; infinity is mathematics. And never the twain shall meet.
My comparison was basically like this:
Assume false thing is true (you can have an infinite amount of a physical object)
Now, we could stop here, and say that is a false can't is true, QEQ. Or we could follow the logic of the flawed system, which i did, and proved that IF the flawed system were true, ie you can have an infinite ammount of money, Then does not matter if they come in bundles of ones or twenties. they would be equal.
But considering the comparison you nitpicked, instead of the core of my argument, you basically argued against a strawman.
But, completely unrelated the the thing i proved, and instead related to the thing you commented on. you can set up the fight to get either team to win due the the property of listable infinities(the kind we have been working with). This is basically applying the distributive law and the axiolm of infinity to DBZ characters.
In a million individual fights between Goku and Krillin, Goku would indeed win.
But if it were instead like an infinite arena with Gokus and Krillins of either side with no surrender. The Goku's would never run out of Krillins to kill, meaning that Krillins would never lose, resulting in the fight never ending, with no victor.
Or we could spread out the Gokus so there are one of them per 100 Krillins meaning the Krillins win. Now you might say "but ther ae more Krillins than Goks" No, not if we are dealing with an infinite ammount of them,just follow the same logic of my first post.
In fast, i even had no reason to defend my comparison because it wasnot the argument.
You could instead construct it like this to avoid ambiguity
"P1: Batman is faster than The flash"
"P2: No, it has been demonstrated on numerous times that the Flash is faster"
"P1: Well, The flash does not exist, you are wrong"
Given the nature of reality none of us is right
But, given the premises of the OP wher infinite ammount of dollar bills exist, i am right
1$ and 20$ are the physical objects aka object A and B with B being 20 times bigger/valuable than A . When you are dealing with infinities you place ground rules else you make no sence because there are different kinds of infinities and this is a proven fact .
www.youtube.com/watch?v=elvOZm0d4H0
Stop breaking the rules and you will find an answer .
The video you posted are comparing the difference between listable and unlistable infinities, and that they are indeed different.
Given an infinite amount of discrete things, like object, like bills, they would both be listable. Meaning that they are the same kind of infinity.
And if you bothered watching the video you linked, you would see, going back to my original proof, i were comparing two listable infinities, and showing that they are the same, wher you argued that two listable infinities were not the same, which is demonstrably false.