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  1. #151
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by dissonance View Post
    "In mathematics, an uncountable set is an infinite set which is too big to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the natural numbers. The related term nondenumerable set is used by some authors as a synonym for "uncountable set" while other authors define a set to be nondenumerable if it is not an infinite countable set."
    -http://wapedia.mobi/en/uncountable


    "Some sets are infinite; these sets have more than n elements for any integer n. For example, the set of natural numbers, denotable by <math>\{ 1, 2, 3, 4, 5, \dots \}</math>, has infinitely many elements, and we can't use any normal number to give its size. Nonetheless, it turns out that infinite sets do have a well-defined notion of size (or more properly, of cardinality, which is the technical term for the number of elements in a set), and not all infinite sets have the same cardinality.

    To understand what this means, we must first examine what it doesn't mean. For example, there are infinitely many odd integers, infinitely many even integers, and (hence) infinitely many integers overall. However, it turns out that the number of odd integers, which is the same as the number of even integers, is also the same as the number of integers overall. This is because we arrange things such that for every integer, there is a distinct odd integer: … ?2 ? -3, ?1 ? ?1, 0 ? 1, 1 ? 3, 2 ? 5, …; or, more generally, n ? 2n + 1. What we have done here is arranged the integers and the odd integers into a one-to-one correspondence (or bijection), which is a function that maps between two sets such that each element of each set corresponds to a single element in the other set.

    However, not all infinite sets have the same cardinality. For example, Georg Cantor (who introduced this branch of mathematics) demonstrated that the real numbers cannot be put into one-to-one correspondence with the natural numbers (non-negative integers), and therefore that the set of real numbers has a greater cardinality than the set of natural numbers.

    A set is countable if: (1) it is finite, or (2) it has the same cardinality (size) as the set of natural numbers. Equivalently, a set is countable if it has the same cardinality as some subset of the set of natural numbers. Otherwise, it is uncountable."

    -http://wapedia.mobi/en/countable

    Again, a set is countable if it has a one to one correspondence with the natural numbers. For example, multiples of 7 are countable because you can come up with a formula which corresponds that set with the set of natural numbers. Both sets are infinite, but they are, by definition, countable.
    Where is the contradiction in here with one of my claims?

    Quote Originally Posted by dissonance View Post
    "A set is countable if: (1) it is finite, or (2) it has the same cardinality (size) as the set of natural numbers. Equivalently, a set is countable if it has the same cardinality as some subset of the set of natural numbers. Otherwise, it is uncountable."]
    I am sure your Ni world could exonerate your thinking from this contradiction.

    Finite here is a requirement for countability. Infinite is the antonym of finite. Infinite does mean non-countable.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

    “No man but a blockhead ever wrote, except for money.”---Samuel Johnson

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  2. #152
    desert pelican Owl's Avatar
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    Quote Originally Posted by BlueWing View Post
    1)Infinity-As aforementioned, by definition has no limits. Therefore, it is not possible for us to have a conception of anything that is infinite. We can only have a symbol for an infinity but not a direct representation thereof. Exactly like in Kant we get that all we know about the noumenal world is that it exists, but not any particular thing about it.

    Here again, is the reason why, an entity that is unbounded (which is infinite by definition) will occupy all things, simply because there is nothing to prevent it from doing so.
    You also said that that which is infinite is not countable. This definition makes much more sense to me because it's more general; e.g., it allows for the existence of mathematical infinites, both of which are not countable, but, nevertheless, are unequal in size. (The set of all real numbers is 'larger' than the set of natural numbers b/c there is no way to create a bijection/one to one function between them.) It also admits for the possibility for an infinite entity that occupies all things, but it does not entail that this entity exists. It seems I can conceive of an uncountable infinite that is not unbounded, i.e, an infinite that is limited--such as the set of natural numbers, or an eternal rock, or God.


    Quote Originally Posted by BlueWing View Post
    The onus is on you to prove that it is plausible to believe that nothing can come from nothing because otherwise the principle of existence cannot be justified.
    I don't believe something can come from nothing. I was refering to a theistic concept that states that God, by his eternal power, caused temporal beings to come into existence, not from some pre-existent substance, but from nothing. It's not something from nothing; it's something from God.

  3. #153
    Occasional Member Evan's Avatar
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    The set of rational numbers between zero and one is uncountable, BW. Does that mean it encompasses all numbers?

    The set of integers (..., -2, -1, 0, 1, 2, ...) is countable. Does that mean it is not infinite?

    Take a math class please, you're just embarrassing yourself.

    Quote Originally Posted by BlueWing View Post
    Infinite does mean non-countable.
    Wrong.

    God dammit, where are the math people to back me up here?

  4. #154
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by Owl View Post
    You also said that that which is infinite is not countable. This definition makes much more sense to me because it's more general; e.g., it allows for the existence of mathematical infinites, both of which are not countable, but, nevertheless, are unequal in size. (The set of all intergers is 'larger' than the set of natural numbers b/c there is no way to create a bijection/one to one function between them.) It also admits for the possibility for an infinite entity that occupies all things, but it does not entail that this entity exists..
    If such an entity does not exist, how does anything exist? If all entities are finite, it means they were created by something else. Where did it all start?




    Quote Originally Posted by Owl View Post
    I don't believe something can come from nothing. I was refering to a theistic concept that states that God, by his eternal power, caused temporal beings to come into existence, not from some pre-existent substance, but from nothing. It's not something from nothing; it's something from God.
    If God created the universe, who created God? We go ad infinitum in the search for the first cause as I have remarked above.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

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  5. #155
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by dissonance View Post
    The set of rational numbers between zero and one is uncountable, BW. ??
    Yeah, you know. Just like there is 2100 miles between Detroit and LA, but the miles between here and there are uncountable.

    An interesting point to be derived from this however is, the exact value of some numbers for example (3.6677777 or any number where we cannot find the exact last digit of) is considered non-rational (or could not be expressed in a fraction) because the last decimal could easily stretch to infinity. This does not make the number itself infinite. The exact value of this particular number may be uncountable, and therefore infinite, however, in light of the class this number inhabits, the value is finite. As the notation we use is, 3.67 (not 3.677777777777).

    Quote Originally Posted by dissonance View Post
    The set of integers (..., -2, -1, 0, 1, 2, ...) is countable. Does that mean it is not infinite??
    The entire set of natural numbers may be infinite, not all sets of natural numbers are infinite.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

    “No man but a blockhead ever wrote, except for money.”---Samuel Johnson

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  6. #156
    Occasional Member Evan's Avatar
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    Quote Originally Posted by BlueWing View Post
    Yeah, you know. Just like there is 2100 miles between Detroit and LA, but the miles between here and there are uncountable.



    The entire set of natural numbers may be infinite, not all sets of natural numbers are infinite.
    Again, you are just making yourself look ignorant. You're only right in your own mind.

    I see what you're getting at, but your use of terms is blatantly incorrect. Your refusal to switch terms makes you impossible to discuss anything with.

    And your condescension makes you look like an asshole and shows your F side.
    Last edited by Evan; 09-28-2008 at 12:44 PM. Reason: mean.

  7. #157
    desert pelican Owl's Avatar
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    Quote Originally Posted by BlueWing View Post
    If such an entity does not exist, how does anything exist? If all entities are finite, it means they were created by something else. Where did it all start?


    If God created the universe, who created God? We go ad infinitum in the search for the first cause as I have remarked above.
    God is infinite, yet not all is God.

    It seems you're having trouble accepting that an infinite being can be limited.

    If something is infinite it may be asked in what sense that thing is infinite. Is it infinite in size? Is it infinite in duration? Is it infinite wisdom?

    Why can't something be infinite in one quality, but limited in another? There's no contradicion in asserting that a rock is infinite in duration but not in size, so what reason do I have for rejecting its possible existence? Or why should it be impossible for a God of infinite duration, power, and wisdom to exist as a serparate substance from the things it creates?

  8. #158
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by Owl View Post
    God is infinite, yet not all is God.

    It seems you're having trouble accepting that an infinite being can be limited.

    If something is infinite it may be asked in what sense that thing is infinite. Is it infinite in size? Is it infinite in duration? Is it infinite wisdom??
    Infinite by definition means without bounds.

    Pay special attention to definitions 3 and 8.

    infinite definition |Dictionary.com

    Sometimes, however, infinity is used in a figurative fashion, and not in its linguistically precise. In those contexts it means something very large, so large that it is difficult to imagine how it could be measured. In those case, the notion the author has in mind is a very large finite entity, but because it is possible to be measured (though difficult), it is finite.

    In other cases (as has been much practiced by literary artists) infinite is used as a superlative term to praise how much one values a quality. (For example, as you mention, infinite wisdom, or as someone may say 'infinite love'.) The less said on this usage of the term 'infinite' the better, on that note I shall stop at this point.



    Quote Originally Posted by Owl View Post
    Why can't something be infinite in one quality, but limited in another? There's no contradicion in asserting that a rock is infinite in duration but not in size, so what reason do I have for rejecting its possible existence? Or why should it be impossible for a God of infinite duration, power, and wisdom to exist as a serparate substance from the things it creates?
    Nothing in this world is infinite for this reason. If something were to be infinite, it would be in infinite size. As this is the only way it is conceivable for an entity to occupy all things. If something were infinite in this world, it would be of infinite size or all things, as this is the only way an entity can be clearly without boundaries. Infinite duration? In the world where we have one element which occupies all things, there would be no time either. As time is a division of occurences into measurable periods. In the world of infinity, an entity simply is, it is not going anywhere. Moreover, an ifinite entity is by definition inseparable, time by definition of itself separates entities into fragments of occurences.

    Infinite wisdom? Not possible. Knowledge requires the knower and the known (as established by Schopenhauer), this contravenes the definition of infinity because this scenario presupposes 2 entities instead of one.

    Infinite power? Power implies the one holding power and the one obeying power. Same problem.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

    “No man but a blockhead ever wrote, except for money.”---Samuel Johnson

    My blog: www.randommeanderings123.blogspot.com/

  9. #159
    Senior Member LostInNerSpace's Avatar
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    Quote Originally Posted by BlueWing View Post
    Axiom: The Universe is Infinite, therefore the existence of God is impossible independent of the existence of the world.

    Infinity: Continuous, incessant flow of entities.

    This world is finite because not all things in this world are continuous, if they were, they all would be part of the same entity.
    You are thinking within the confines of the human mind/experience. "Finite" assumes our notion of time is real. It's real only because we perceive it to be so. We are not capable of perceiving any other scenario--not yet anyway. We can, however, imagine other scenarios.

    Think about it this way. Where did all of this "finite" stuff in our universe come from? Given the vast size of the universe, it seems impossible that anything beyond what we perceive could possibly exist. But what if our universe is one of an infinite number of other universes spread out in distances comparable to the distances we see in our universe, only scaled up to the size of what lies beyond. We are looking from inside our universe. All we can see is our universe. Kind of like being trapped in a marble in an infinitely large pile of other marbles. Think of the different universes spread out like stars in our universe. Assuming the infinite number of universes theory is correct, where did (they) originate? To me, "God" is the unknown. I don't like the term "God" because it implies something we can perceive in terms of our own limited existence.

  10. #160
    no clinkz 'til brooklyn Nocapszy's Avatar
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    Quote Originally Posted by BlueWing View Post
    I did read your post. I will be very impressed if you will be able to explain how it is possible for a finite entity to create itself. Try again.
    You obviously didn't read my posts, otherwise you'd know that I don't assert that a finite entity can create itself -- there's no actual rule saying one way or the other, it's just that we've never seen it happen so we like to assume they can't.

    Anyway, my point was, if the universe, as you say, being infinite, always existed (you'd be in pretty staunch disagreement with... well, every scientist anywhere) then the same cane be said about God. Let's say God always existed, just like you propose the universe did. Then he could have existed long enough to create the universe, thereby making it less than infinite, thereby toppling your entire stance.

    You don't know that the universe is infinite. It is, at the very best, a good guess.
    we fukin won boys

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