Actually that number can be written in fraction form.
Yes, a set that has finite length is finite.A series that never ends is infinite. 1,2,3,4,5,6,7....(and on forever) Yet, a set that does end, no matter at how high of a number ought to be called finite.
No. You just quoted the definition. Countable means one to one correspondence with the natural numbers (which is an infinite set).Thus, as for the use of the word uncountable, the only reason something would be uncountable is if it is too great to be counted.
Wow, you've totally misunderstood what you were reading. The "counting numbers" is the set of numbers [1, 2, 3, 4, ...(to infinity)]. That is an infinite set. It is a COUNTABLE infinite set. Any set that has a one to one correspondence is also called an infinite set. An example would be [5, 8, 11, 14, 17...(to infinity)] which corresponds to the counting numbers by multiplying by 3 and adding 2. That is also an infinite set that's countable. Any set that you can write a function for on a computer that corresponds to the counting numbers is countable. An example of an uncountable set is the set of all numbers from 1 to 2, because for each function you come up with, you can think of a number that throws it off.Thus, clearly, as stated in the opening paragraph, a finite set is one that has one to one relations with natural numbers. Basically, one that could be expressed in terms of basic numbers, like 4,5,6,7, and so on. No question here, these numbers as entities in themselves are finite, and perhaps the entire collection of such numbers will be as well.
@Bolded statement  Nope.Later in the chapter (3.6), it turns out that there are two kinds of infinite sets, countable and uncountable. The only reason why an entity is uncountable is if it is too large to be counted, and this Rodgers refers to as the 'higher levels of infinity'. Yet, the countable 'infinite' sets are indeed merely very large sets. This is exactly what Rodgers in the opening paragraph stated that 'infinite' does not mean.
LOL. Mathematicians know exactly what countable means, and I can assure you they will not call it "a very large set". It means an infinite set that corresponds to the counting numbers (again, an infinite set) OR a set of finite size.In summary, from the standpoint of descriptive linguistics, infinite, by most mathematicians is regarded as a very large set, which appears to be never ending.
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Thread: Why I do not believe in God

09292008, 12:06 PM #171

09292008, 12:12 PM #172

09292008, 12:19 PM #173
No. Not irrational numbers. Like Pi, or E, or the square root of 2.
And if you look at the numbers after the decimal place, those numbers are an example of an uncountable infinite set.
Edit: Anyways, the definition of countable really doesn't matter in this argument. BW said something that does not have a beginning or an end takes up all things. What he forgets is that it only takes up all things in the dimension that it exists in. So a line takes up all points in the one dimension of its existence. A plane takes up all points in the two dimensions of its existence.
He must be talking about a four dimensional (3 directional dimensions AND time) infinite. Or an infinite in spacetime, I guess you could call it..
He's only been talking about an infinite in time, though, which need not take up any point in 3dimensional space.

09292008, 12:28 PM #174

09292008, 12:29 PM #175
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It's like...an algebraic fraction. I think Pi is called a "real" number, but I'm not sure.

09292008, 12:34 PM #176

09292008, 12:37 PM #177

09292008, 12:38 PM #178
We really don't dude... I mean... I'm not like a damned genius with math, but I know enough to know that BW doesn't know shit, and that he's completely utterly wrong in his assertion, and I also know enough to know there are no undermining theories that might change my stance.
we fukin won boys

09292008, 12:39 PM #179
Ah. Well the problem is, you can't calculate the circumference and the diameter exactly enough (you need Pi, lol). So you can't write it in fraction form.
Edit: to clarify.
Circumference = 314
Diameter = 100
Pi = 3.14
Circumference = 314159265358979
Diameter = 100000000000000
Pi = 3.14159265358979
You can keep adding decimal places, but you will never be able to represent the exact number that is Pi with division. Each time you try, you can think of a more exact fraction.
Same metaphor holds for countability.
5/7 can be represented in fraction form, obviously. That means you can represent the exact number on a computer. =.714285 (repeating). The amount of numbers after the decimal is infinite, but you can make a computer function that calculates the next number from the number before. Therefore it is countable.
If you can't make that function, it is uncountable. For example, you can't make a function for Pi. Uncomputable is the same thing as uncountable. Alan Turing came up with a good example of an uncomputable function (the halting problem, or universal debugger).
True, but I'd rather have some backup so that BW doesn't call me "Ni crazy" and tell himself that he's right anyway.
Edit 2: Back to the point  As I said before, something that is infinite covers all things IN ITS DIMENSION. But that doesn't mean ONLY infinite things cover all things in the dimension.
Example: you have a number line, and a bunch of points scattered along, say between 100 and 100. Well, a line in that dimension will cover all those points. But so will a line segment (which is finite). The line segment from 101 to 101 covers all the points. Each time you add a point, you can still come up with a FINITE line segment that covers all the points. So to cover all atoms in space, you don't need an infinity in spacetime. You only need a metaphorical line segment (in however many dimensions the universe has) that includes all the atoms in space.
We know (in science) that the amount of matter/energy in the universe is constant. Matter/energy cannot appear out of nowhere and cannot disappear into nothingness. Therefore the exact same amount of matter/energy that we have in the universe now must have always existed, and must always exist. I think this is enough to prove that, at least in the time dimension, the universe is infinite (the universe defined as the smallest linesementish thing covering all points in spacetime).
If this value, this amount, of matter/energy stays exactly the same forever, we can conclude that it is finite. There is ONE exact value for this amount. Infinity is not an exact value, it is a description of a trend. So if it has a value, it's finite. The matter/energy in the universe is finite.
In order to cover all of this finite amount of stuff, we only need a finite universe (in the directional dimensions). An infinite universe would do the trick, too, but we may as well make the bounds as small as they can be without losing information. So lets call the universe the (however many dimensional) line segment that covers all matter/energy.
No need for infinity in the directional dimensions, only in the time dimension. This is not an impossibility at all.
Picture a line (infinite length). Now put this line somewhere on a Cartesian plane. In one dimension, it is infinite, in another, it is completely finite. We could also think of a box that has infinite width and a finite height.
I guess my point is, you only need infinity in time. That does not at all imply infinity in space.
But whatever, all of the above is really just nitpicking. If God were to exist, he could not have "created" the universe, because "create" implies finite in the time dimension, which we know is not possible (Unless you want to change the definition of universe to be something other than allinclusive, or unless we want to question the law of conservation of matter/energy). If God did exist, he would have to exist as a subset of what we call the universe, because the universe is defined as containing all things. I guess God could be defined as the exact same set as the universe, but then whenever we say "God", we could just replace it with "universe".
That's about as far as I've ever gotten. I can believe in God if we define God as the universe. Otherwise, it seems like a nonsense idea. And even then, no one else uses that definition of God, so I just call myself an atheist. The whole concept of "creating the universe" is a nonsense idea anyway.

09292008, 05:35 PM #180
I know dude, but the numbers they're dividing to find those decimal places are the fraction. I thought it was like something close to 22/7 but not exactly that. anyway it's not a decimal it's a fraction.
either way your point still remains, and blue's doesn't.we fukin won boys
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