I went when I was really young. I think I mainly visited resorts and amusement parks.
Infinity….
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So, let’s have a look again, and let’s take tis look from a “game theory” point of view in the sense that there exist different strategies:
(but first some words about infinity that already have been mentioned here:
there are as many natural numbers, as there are even or odd numbers (even though even plus odd makes up the naturals). There are as many integer numbers as there are natural numbers, even though the naturals are “only” the positive branch of the integers. There are as many fractions (rational numbers) as there are naturals. This all comes from Cantor’s diagonal argument. These sets are called “countable infinite” sets, because you can map them one-on-one onto the natural numbers which you could count (if you have infinite time that is). The “real numbers”, which are the rationals plus irrationals (like Pi, e, 2^(1/2) which cannot be expressed by fractions), cannot be mapped in such a way. This is an “uncountable infinite” set, and there are more reell numbers than naturals.)So, let’s look at our two players (A and B) and different strategies (for simplicity i assume both A and B be male)
(1) A gives B ascending numbers (starting with one, not giving back a number that B already had), B gives A his lowest number:
So, it will look like that:
A -> B: 1,2
B -> A: 1
A -> B: 3,4
B -> A: 2
etc.
B will give back all numbers back to A, having an empty bag at the end (2*“amount of naturals”=“amount of naturals”!), A will have all numbers.(2)A gives B his lowest numbers (inlcuding those given beforeand handed back), B gives A his highest number.
A -> B: 1,2
B -> A: 2
A -> B: 2,3
B -> A: 3
etc.
So, A will have given all numbers to B, and end up with an empty bag, while B has all natural numbers.(3)A gives B his lowest numbers (inlcuding those given beforeand handed back), B gives A his lowest number.
A -> B: 1,2
B -> A: 1
A -> B: 1,3
B -> A: 1
etc.
So, A will have given all numbers to B, and end up with an empty bag except for the “1”, while B has all natural numbers, except for the “1”.(4) A gives even numbers, B does anything:
A will have all odd numbers at least, regardless of B’s strategy. So, A has an infinite amount of numbers. The exact amount of B depends on what B does.So, the answer:
you can’t tell, unless you know how they choose to give and give back numbers. It can be anything from nothing over any finite number (by changing strategies halfway) to an infinite amount. -
“So, the answer:
you can’t tell, unless you know how they choose to give and give back numbers. It can be anything from nothing over any finite number (by changing strategies halfway) to an infinite amount.”Greaaaattt… I hate questions without any right “answers,” but I wasn’t that off with “Mr. Zero.” :wink:
“Hm, Germany won the quarterfinal ?”
Well, football is European sport (well South America, too!) so we expected to lose. But next time, we will be out for blood! :wink:
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@F_alk:
So, let’s have a look again, and let’s take tis look from a “game theory” point of view in the sense that there exist different strategies:
(but first some words about infinity that already have been mentioned here:
there are as many natural numbers, as there are even or odd numbers (even though even plus odd makes up the naturals). There are as many integer numbers as there are natural numbers, even though the naturals are “only” the positive branch of the integers. There are as many fractions (rational numbers) as there are naturals. This all comes from Cantor’s diagonal argument. These sets are called “countable infinite” sets, because you can map them one-on-one onto the natural numbers which you could count (if you have infinite time that is). The “real numbers”, which are the rationals plus irrationals (like Pi, e, 2^(1/2) which cannot be expressed by fractions), cannot be mapped in such a way. This is an “uncountable infinite” set, and there are more reell numbers than naturals.)So, let’s look at our two players (A and B) and different strategies (for simplicity i assume both A and B be male)
(1) A gives B ascending numbers (starting with one, not giving back a number that B already had), B gives A his lowest number:
So, it will look like that:
A -> B: 1,2
B -> A: 1
A -> B: 3,4
B -> A: 2
etc.
B will give back all numbers back to A, having an empty bag at the end (2*“amount of naturals”=“amount of naturals”!), A will have all numbers.(2)A gives B his lowest numbers (inlcuding those given beforeand handed back), B gives A his highest number.
A -> B: 1,2
B -> A: 2
A -> B: 2,3
B -> A: 3
etc.
So, A will have given all numbers to B, and end up with an empty bag, while B has all natural numbers.(3)A gives B his lowest numbers (inlcuding those given beforeand handed back), B gives A his lowest number.
A -> B: 1,2
B -> A: 1
A -> B: 1,3
B -> A: 1
etc.
So, A will have given all numbers to B, and end up with an empty bag except for the “1”, while B has all natural numbers, except for the “1”.(4) A gives even numbers, B does anything:
A will have all odd numbers at least, regardless of B’s strategy. So, A has an infinite amount of numbers. The exact amount of B depends on what B does.So, the answer:
you can’t tell, unless you know how they choose to give and give back numbers. It can be anything from nothing over any finite number (by changing strategies halfway) to an infinite amount.see, the problem with this question is that it is in essence non-sensical. If you have an infinite amount of activities, one taking place with every division before noon, then in theory you could never reach noon (i know that you said that we can in this example, but it still makes little sense that we could reach noon assuming an infinite number of time-divisions).
Anyway, this got me to thinking - assuming there is an infinite number of divisions of time before noon, how do we ever reach it? Or is noon still a theoretical idea, and i choose to eat my sandwich at some arbitrary (increasingly longer) fraction of the way towards noon? Or is it that our non-spatial, yet linear travel through time have an increasing velocity that approaches infinity relative to noon as we approach noon?
These are some of the things i think about when i’m jogging or biking. -
Greaaaattt… I hate questions without any right “answers,” but I wasn’t that off with “Mr. Zero.”
Did somebody say my name? 8)
Of course if you want an answer, I like to call upon a little friend I like to call, “Mr. Zero.” Case closed!
I’m glad someone believes in my abilities. :oops:
Sorry, couldn’t resist the play on my name.
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Ha, well you won’t know how many many times I “play” on my name :wink:
Yep, I parted the Red Sea 8)
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I agree with your answer, but you will have to admit it is a little strange… We are not suppose, in arithmetic, to consider those thing like the order in wich we distribute numbers… x(x - 1) = x^2 - 1x and x + 2x = 3x, whatever the manner you distribute the x + 2x, it would give 3x… Also the “Infinity is not equal to Infinity” thing is a problem that can only be very, very partialy resolve with Cantor theory of different type of infinity… the resolution also make us ask some strage question, like “is there is other infinity between Aleph 0 and Aleph 1 ?” Anyway, i don’t know if infinity really does exist, maybe, like Poincaré, Gauss & Kronecker thinking, infinity does not exist, it is just potential… But it seem it is not the case…
Damn Cantor, Gauss said infinity was just problem ! :)
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“I agree with your answer, but you will have to admit it is a little strange… We are not suppose, in arithmetic, to consider those thing like the order in wich we distribute numbers… x(x - 1) = x^2 - 1x and x + 2x = 3x, whatever the manner you distribute the x + 2x, it would give 3x… Also the “Infinity is not equal to Infinity” thing is a problem that can only be very, very partialy resolve with Cantor theory of different type of infinity… the resolution also make us ask some strage question, like “is there is other infinity between Aleph 0 and Aleph 1 ?” Anyway, i don’t know if infinity really does exist, maybe, like Poincaré, Gauss & Kronecker thinking, infinity does not exist, it is just potential… But it seem it is not the case…
Gauss said infinity was just problem”Well, I am sure that Cantor believed in actual infinite numbers transfinite numbers. However, I have not seen an example of actual infinity thus far, except if you believe space is continuous. For Aleph 0 and Aleph 1, Cantor believed in the Continuum hypothesis or Generalised Continuum hypothesis, which would seem to imply no. But Cantor’s hypothesis was independent of the other set-theory axioms, so who knows? :roll: I might use the Axiom of Choice, though this might lead up to some strange paradoxes. Perhaps, these cardinalities just ‘float around in an annoying way.’ Maybe Monsieur FinsterniS is right on Gauss, ‘just keep infinity out of mathamatics!’ :D
PS: I find it amusing, yet appalling, to see learned mathematicians fight among each other, especially the terrible war waged between Georg Cantor and Leopold Kronecker.
‘I see it but I don’t believe it.’ ~ Georg Cantor
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@TM:
Well, I am sure that Cantor believed in actual infinite numbers transfinite numbers. However, I have not seen an example of actual infinity thus far, except if you believe space is continuous.
In fact there is a lot of exemple of infinity. You won’t see a lot of Aleph 0, but a lots of Aleph 1 !
For Aleph 0 and Aleph 1, Cantor believed in the Continuum hypothesis or Generalised Continuum hypothesis, which would seem to imply no.
Continuum Hypothesis is true when you look only at it as an axiom to base other sets, but false when you look at math as only abstaction… (it is often the inverse). Anyway i don’t trust infinity, as one of my teacher said; we would need a new logic to understand infinity, often you come up with the conclusion it is False, then you look at another way and it is True… Just like the continuum hypothesis…
Maybe Monsieur FinsterniS is right on Gauss, ‘just keep infinity out of mathamatics!’ :D
Well no, i don’t agree with Gauss this time, i think it was just too frustrating for him… Like it is now for us anyway, if nobody around me were talking about Infinity i would never have think of it; too strange. But Gauss was right that infinity is just a lots of problem.
PS: I find it amusing, yet appalling, to see learned mathematicians fight among each other, especially the terrible war waged between Georg Cantor and Leopold Kronecker.
Don’t forget Cantor’s allies; Hilbert, Dedekind, Godel…
And also don’t forget the “potential infinity” fidels; Poincaré, Weyl, Brouwer
… -
“Don’t forget Cantor’s allies; Hilbert, Dedekind, Godel…”
Lets not forget Mittag-Leffler and Weierstrass. But I favor Dedekind, really stuck by him to the end when Cantor was at his worst.
“In fact there is a lot of exemple of infinity. You won’t see a lot of Aleph 0, but a lots of Aleph 1 !”
She probably means in real life. I’m am still unsure if there can be an actual infinity in real life? Potential more like it.
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Being pragmatic by nature, I don’t like these kind of questions. I personally like ones based in reality, not mathmatical theory. Oh well.
Where did your name come from. Moses?
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Well, I had a friend who called himself Jesus. So I donned the name Moses, and that is history :P
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Just be careful…cause if you blink, you might miss the fact that it is now 1 sec past noon.
SUD
but this is a relative noon. A noon that we created. How do we know that it is not a fraction of the temporal distance to the real noon - the one that we will never reach? Just because you call it “noon” doesn’t mean that it really is so.
Oh this hurts my head. Time to go cycling :) -
“In fact there is a lot of exemple of infinity. You won’t see a lot of Aleph 0, but a lots of Aleph 1 !”
Herrn FinsterniS,
My knowledge of science and mathematics is very limited, but I have come to believe that infinity can only exist in one’s mind. I have only witnessed potential infinity, not actual infinity. Can you please correct me if I am wrong?“but this is a relative noon. A noon that we created. How do we know that it is not a fraction of the temporal distance to the real noon - the one that we will never reach? Just because you call it “noon” doesn’t mean that it really is so.”
I tried to solve this equation myself, but I also ran into some of Sir Crypt’s questions. I do not think you can ever traverse an infinite number of sets.
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@TM:
Herrn FinsterniS,
My knowledge of science and mathematics is very limited, but I have come to believe that infinity can only exist in one’s mind. I have only witnessed potential infinity, not actual infinity. Can you please correct me if I am wrong?Then you would side with Poincaré…
Well, the time continuum and the space continuum can be consider an exemple of infinity as you can always divide any time/space by 2 (or any other numbers…). If you cannot divide an X distance by 2, then an atom that move does’nt move, it teleport itself between X and X+1 because there is nothing between X and X+1… Also an atoms is made from an infinity of side; like any sphere, circle, curve… Infinity is potential when when we look at numbers, but in time and space it is more problematic.
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@TM:
Herrn FinsterniS,
My knowledge of science and mathematics is very limited, but I have come to believe that infinity can only exist in one’s mind. I have only witnessed potential infinity, not actual infinity. Can you please correct me if I am wrong?Then you would side with Poincaré…
Well, the time continuum and the space continuum can be consider an exemple of infinity as you can always divide any time/space by 2 (or any other numbers…). If you cannot divide an X distance by 2, then an atom that move does’nt move, it teleport itself between X and X+1 because there is nothing between X and X+1… Also an atoms is made from an infinity of side; like any sphere, circle, curve… Infinity is potential when when we look at numbers, but in time and space it is more problematic.
having trouble with this one. I can readily imagine atoms, however they are more like little planets with orbits around them, at the same time, their centers are not necessarily completely spherical - only somewhat, depending on their atomic number. The orbitals, of course made up of electrons, are not spherical either, but may be in a variety of shapes depending upon valencies, etc.
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They do not need to be sperical, they only need to have a curve somewhere in their design, a cylinder is’nt a sphere it still got an infinity of sides. Any curse is made of an infinity of side, if you take a sphere, or a cylinder, well any kind of geometric form with curve; you well get an infinity of side.
If we look at the geometric form composign the mouvement of an electron around the atom, what would we get ? 4 sides ? 6 sides ? or an infinity of sides because it is a curve ?
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No because this topic :lol:
Spock!..…Spock! -
They do not need to be sperical, they only need to have a curve somewhere in their design, a cylinder is’nt a sphere it still got an infinity of sides. Any curse is made of an infinity of side, if you take a sphere, or a cylinder, well any kind of geometric form with curve; you well get an infinity of side.
If we look at the geometric form composign the mouvement of an electron around the atom, what would we get ? 4 sides ? 6 sides ? or an infinity of sides because it is a curve ?
fair enough.
the orbit of the electron does tend to be circular, and the atoms tend to be represented as spherical (although i’m not sure they exactly are that).And Ghoul - that’s enough “logic-seeking” out of you. You know this is an illogical series (although based on a pseudo-logic given imaginary circumstances . . . ).
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@cystic:
They do not need to be sperical, they only need to have a curve somewhere in their design, a cylinder is’nt a sphere it still got an infinity of sides. Any curse is made of an infinity of side, if you take a sphere, or a cylinder, well any kind of geometric form with curve; you well get an infinity of side.
If we look at the geometric form composign the mouvement of an electron around the atom, what would we get ? 4 sides ? 6 sides ? or an infinity of sides because it is a curve ?
fair enough.
the orbit of the electron does tend to be circular, and the atoms tend to be represented as spherical (although i’m not sure they exactly are that).And Ghoul - that’s enough “logic-seeking” out of you. You know this is an illogical series (although based on a pseudo-logic given imaginary circumstances . . . ).
Hehe :lol:
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@cystic:
the orbit of the electron does tend to be circular, and the atoms tend to be represented as spherical (although i’m not sure they exactly are that).
Not really :)
The “orbit” idea is the so called Bohr-model of atoms. It is the very very first quantum model.
And it’s wrong :)
if the electrons really orbited the nucleus like planets the sun, then we would have a lot of trouble, explaining why this constantly accelerated charge does not emit em-waves all the time, lose energy by that and drop into the nucleus.
As well: There are many states for electrons, where they don’t have any angular momentum: they don’t “fly around”.Bohr’s picture is nice, for a first understanding, but you should always remember that it is actually wrong (even if you can explain some things through it).
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