tell me about infinity

[nerve]

I'm in the middle of reading a book called "The Case for a Creator" by Lee Strobel, and in one of the interviews, an argument that is supposed to disprove infinity is brought up. it goes like this: I have infinity marbles and I decide to give them to you. you then have infinity marbles, and I have zero. or, I give you all of the odd numbers, and keep the even. you then have infinity marbles, and I also have infinity marbles. or, I give you all of the marbles four and up, and so you have infinity marbles, and I end up with three. in the first case, infinity minus infinity is zero, in the second case, infinity minus infinity is infinity, and in the last case, infinity minus infinity is three. since in each case, the same number is subtracted by the same number and comes out with different results, it is mathematically impossible. but I don't see it. maybe it is mathematically impossible, though, in the book, I think they try to say that infinity is not possible at all. +shrug+ the problem I see with it (as best as I can understand this) is that, in each case, I would never be able to give you that amount of marbles, I would always be giving them to you. is that not the idea of infinity? not...finite? to me, it seems like the example treats it as something finite. appearently I'm wrong. the reason I even made this thread is because I brought this up last night to a friend of mine and he shot my suggestion down instantly and said that I was involving time, and it isn't a matter of time. he didn't seem to want to explain it to me, so I just dropped it. he also has an IQ of 182. I felt pretty dumb. I think my problem might just be that I'm confusing the mathematical impossibility with actual impossibility, but then, what is the difference? doesn't math depend on time? help me out, please :(

[CoLd BlooDed]

Well, what about an infinite amount of time? I could care less if a kid with an IQ of 182 tried to shoot me down... unless he could prove it?

[Ynot]

first off, it would be infinite marbles, rather than infinity marbles you could never give me infinite marbles, it would take infinite time infinity isn't a number it's the inability to comprehend the scale of something you can't do calculations on an undefined value

[nerve]

first off, it would be infinite marbles, rather than infinity marbles you could never give me infinite marbles, it would take infinite time right. I didn't think about that. that's how in is worded it in the book. infinity isn't a number it's the inability to comprehend the scale of something you can't do calculations on an undefined value so the illustration is meaningless?

[wasup]

I'm in the middle of reading a book called "The Case for a Creator" by Lee Strobel, and in one of the interviews, an argument that is supposed to disprove infinity is brought up. it goes like this: I have infinity marbles and I decide to give them to you. you then have infinity marbles, and I have zero. or, I give you all of the odd numbers, and keep the even. you then have infinity marbles, and I also have infinity marbles. or, I give you all of the marbles four and up, and so you have infinity marbles, and I end up with three. in the first case, infinity minus infinity is zero, in the second case, infinity minus infinity is infinity, and in the last case, infinity minus infinity is three. since in each case, the same number is subtracted by the same number and comes out with different results, it is mathematically impossible. This is wrong... The first case, yes, infinity minus infinity is zero. Any number minus itself is 0. However, I am assuming here infinity is EVEN A VALUE. As Ynot said, it's not. It is silly to do a calculation with inifinity, since it is not a value. However, we are doing this calculation on a purely conceptual level. The second case is wrong. You are not giving your friend all your marbles, therefore it is not infinity minus infinity. Realize that infinity plus minus divided or multiplied by any value is infinity. So the real thing you are "calculating" here is infinity/2. Because you are giving her all your odd marlbes, and therefore half of your marbles, it is infinity/0. In the third case, you are not subtracting infinity necessarily, you are subtracting infinity minus the (inexistant) value which makes it 4 and that makes it equal to 3. Regardless, infinity is not a "value" so applying mathematical properties directed at numbers with actual values does not necessarily work. My math teacher rants and raves about infinity, talking about whole like classes being taught about it. Speaking of infinity... Well, take the way to convert a decimal into a fraction. Take the decimal .3 with a dash over the 3 (indicating a repeating decimal). To convert it, we say x=.3 repeating which means 10x=3.3 repeating Subtracting the equations, we get 9x=3 Therefore x = 3/9 or 1/3. Right? Now take .9 repeating. This is .9 with 9 an infinite amount of times. Now, this means it never reaches 1, but becomes infinitely close to 1, right? Well, let's convert that to a fraction... x=.9 10x=9.9 9x=9 x=9/9=1 So .9 repeating = 1? .9 repeating is an infinitely long way to write 1, then.

[Spartiate]

Freaky things can happen when you attempt to use infinity as a number, you can end up with stuff like 1 = 2 and other impossible paradoxes...

[R.D.735]

What is clearly being dealt with are infinite series, not infinity itself. The infinite series consisting of all integers contains the infinite series of odd integers and the infinite series of even integers. The sums of all three infinite series are infinity, but when each is written as a distinct summation, the counter-intuitive results are perfectly reasonable: any divergent series can be expressed as the sum of multiple divergent series. The hypothetical situation does reveal some of the reasons why early mathematicians never developed calculus, though. Infinity is undefined, and that causes problems when one tries to use it algebraically.

[Replicon]

The reason that argument is entirely flawed is, among other things, that its author clearly has no understanding of what "infinite" means. Infinity is NOT A NUMBER!!! It's the concept of there being no limits. "Infinite" doesn't mean "there is a number right after 'infinity-1', called infinity, which is the last number"... it means "pick any number, no matter how large, and I can always give you a larger number". It's sad to see an "infinity - infinity" argument come from someone who claims to be educating his readers on the nature of the universe. For someone who's arguing for a creator, he sure has an inability to understand abstract concepts (not to mention basic high school math).

[Amethyst Star]

I have this book but haven't read it, so I don't know the context of the passage. However, it sounds to me that Stroble is trying to make a point that the idea of an all-powerful God is not illogical or unreasonable, but that He (or whichever pronoun you choose) is beyond logic and reason.

[ClouD]

I have this book but haven't read it, so I don't know the context of the passage. However, it sounds to me that Stroble is trying to make a point that the idea of an all-powerful God is not illogical or unreasonable, but that He (or whichever pronoun you choose) is beyond logic and reason. Logic and reason is based on internal representation. The majority of our species, has a scientifically based IR. Science will always be relative, therefore it is no match to religious thinkings.

[Ynot]

so the illustration is meaningless? in a word, yes

[Goldney]

Infinity is a concept not a number.

[Krrish]

-∞ = 0 = +∞ Simply the number line is a circle meeting at the negative and positive ends.

[Carôusoul]

A poor stonecutter once passed by the king of the land. Upon seeing the riches of the king, the stonecutter marvelled and thought to himself how much he wanted to be as great and powerful as the king. No sooner had he thought this then he was the king. As the king, he was one day walkking in the palace gardens when he felt the sun burning his neck. He looked up and thought to himself how much he wanted to be as great and powerful as the sun, which could burn even him, the king. As before; he was now the sun. As he burned down upon the earth, burning people and killing crops, a dark thunderstorm crossed between him and the earth, rendering him useless. He looked down at the dark storm and thought to himself how powerful it was to hinder him, the great sun. As ever, he became the storm, raging across the land, causing floods and destroying lands. But one day, as he flooded a village with his power, he saw all his lightning and water useless against a great boulder standing in the middle of the village, tall and strong. He thought to himself, how powerful that boulder must be to be entirely unffected by me, the mighty storm. No sooner hasd he thought this, then he was the boulder. At this stage he thought to himself how strong he was, and he, the great boulder was surely the most powerful thing in the land: the sun had no effect on him, neither did the storm or the king. But then one day he felt something down by his side, and upon looking noticed a solitary stonecutter, chipping away. Infinity.

[wasup]

not really carosoul... that's more of a situation of rocks paper scissors And even then the sun still owns all them

[nerve]

and wasup (referring to your first post) hits everyone in the face with the 2x4 of knowledge D: math is not my strongpoint. as soon as you went into your second paragraph my mind was off somewhere imagining little dancing cartoon animals or something. :| Replicon, Ame: they're talking about how the universe had to have a beginning point. I'm not even entirely sure what conclusion they drew from the marble example. here is the rest, maybe you can tell me: "In each case, we have subtracted the identical number from the identical number, but we have come up with non-identical results. "For that reason, mathematicians are forbidden from doing subtraction and division in transfinite arithmetic, because this would lead to contradictions. You see, the idea of an actual infinity is just conceptual; it exists only in our minds. Working within certain rules, mathematicians can deal with infinite quantities and infinite numbers in the conceptual realm. However-and here's the point-it's not descriptive of what can happen in the real world." I was following Craig so far. "You're saying, then, that you couldn't have an infinite number of events in the past." "Exactly, because you would run into similar paradoxes," he said. "Substitute 'past events' for 'marbles,' and you can see the absurdities that would result. So the universe can't have had an infinite number of events in the past; it must have had a beginning. "In fact, we can go further. Even if you could have an actual infinite number of things, you couldn't form such a collection by adding one member after another. That's because no matter how many you add, you can always add one more before you get to infinity. This is sometimes called the Impossibility of Traversing the Infinite. "But if the past really were infinite, then that would mean we have managed to traverse an infinite past to arrive at today. It would be as if someone had managed to count down all of the negative numbers and to arrive at zero at the present moment. Such a task is intuitively nonsense. For that reason as well, we can conclude there must have been a beginning to the universe." ________ there, hopefully that will put it in context. they then mention something about God being outside of time, "but that's a different topic altogether," they say (and I sure hope they cover that later). infinity is such an awesome topic. thanks for all of your replies. :)

[ninja9578]

Infinity is not a number, it's a concept.

[Michael]

I hate thinking about this kind of stuff...

[R.D.735]

The physicists who specialize in the early universe would agree with the conclusion, but not the reasoning. Since time and space are intertwined, the Big Bang represents the beginning of both. Infinity, however, is a poor argument for a finite time-line, since time is only understood to some degree for intervals greater than Planck-time (~10^-47 s). At smaller intervals of time, relativity and quantum theory break down, and time itself becomes an ambiguous concept. It could be continuous, it could be quantized, and it could have a bizarre geometry, all of which complicate the argument that the universe could not have experienced an infinite number of events in time. It may even turn out that time is a contorted spatial dimension(which would help explain relativity).

[orange_entity]

Infinity is a concept and can't be reached (like a number). You name a big number and I could always make it bigger by adding just one. Then there's varying degrees of infinity. I remember back in calculus they mentioned it a lot as being more of a limit thing (infinity minus infinity was undefined I think). I just don't recall right now, so I'm tossing stuff out. I had that argument before with a very bright kid two years ago or so and I just kept showing him proofs and sites. He finally gave up.

[wasup]

when you say there are "degrees" of infinity,I think you mean "magnitude" I'm not I'm not exactly positive what this means to be honest but I do know that there arevarying magnitudes of infinity

[Replicon]

Ok, let's try going through this. I love this kind of discussion. "In each case, we have subtracted the identical number from the identical number, but we have come up with non-identical results. Right off the bat, the ENTIRE premise of his argument is flawed. "infinite" is not a number. We haven't "subtracted an identical number" from anything! That entire sentence (which basically sets the pace for his whole argument) is bogus and flawed. "For that reason, mathematicians are forbidden from doing subtraction and division in transfinite arithmetic, because this would lead to contradictions. You see, the idea of an actual infinity is just conceptual; it exists only in our minds. Working within certain rules, mathematicians can deal with infinite quantities and infinite numbers in the conceptual realm. However-and here's the point-it's not descriptive of what can happen in the real world." This paragraph is irrelevant. He basically states that "infinity is not descriptive of what can happen in the real world" without any supporting evidence/semblance of logic. Next! "You're saying, then, that you couldn't have an infinite number of events in the past." "Exactly, because you would run into similar paradoxes," he said. "Substitute 'past events' for 'marbles,' and you can see the absurdities that would result. So the universe can't have had an infinite number of events in the past; it must have had a beginning. I frankly don't see the relevance. His flawed first sentence about treating "infinity" as a number, showing that it breaks, and claiming without support that that isn't relevant to the real world, somehow translates to there not having been an infinite number of events in the past. "In fact, we can go further. Even if you could have an actual infinite number of things, you couldn't form such a collection by adding one member after another. That's because no matter how many you add, you can always add one more before you get to infinity. This is sometimes called the Impossibility of Traversing the Infinite. He's arguing against the infinite by basically ASSUMING that time is finite and has a beginning. Circular reasoning. "But if the past really were infinite, then that would mean we have managed to traverse an infinite past to arrive at today. It would be as if someone had managed to count down all of the negative numbers and to arrive at zero at the present moment. Such a task is intuitively nonsense. For that reason as well, we can conclude there must have been a beginning to the universe." banana therefore finite universe.

[Carôusoul]

not really carosoul... that's more of a situation of rocks paper scissors And even then the sun still owns all them Rock paper scissors is a circle. circle is infinity my analogy is more rock paper scissors my analogy is infinity QED.

[Identity X]

Rock paper scissors is a circle. circle is infinity my analogy is more rock paper scissors my analogy is infinity QED. Modus Ponens is a brilliant device, but you just bastardised it by using completely nonsense axioms. "Rock papers scissors is a circle" What you're trying to say is "RPS is a cyclical graph with 3 vertices"? RPS is not a circle. It is true that there exists infinitely long paths in such a graph, but that's only one aspect of it. The rest is finite. Saying "RPS [...] is infinity" is therefore a gross simplification and a terribly dodgy thing to say. "Circle is infinity" How? A circle has one edge, and [typically] finite area and a finite circumference. "QED" ...no. I shared the others' concerns about your analogy. It wasn't suitable at all, and therefore ineffectual.

[Carôusoul]

a circle isnt on its own infinite. its about the movement, not the object. its not a static thing. paper>rock>scissors>paper>rock>scissors. Its about the movement.