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  1. #181
    Blah Orangey's Avatar
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    I am really only completely comfortable with EST (easy set theory, hehe), but I know enough to know that BW is correct in his statement that some infinite sets are uncountable because their cardinal numbers are larger than the cardinal number of the set of natural numbers. I think one example of an uncountable infinite set is the set of real numbers (look up Cantor's diagonal argument to see that this is true...not that I even really understand most of the elements of the argument that he presents ).

    So basically, a set whose cardinality is not finite, and is not equal to the cardinality of the set of natural numbers, is uncountable.

    Or if I say it in reverse, an infinite set is countable only if it has cardinality equal to that of the set of natural numbers (i.e., aleph-null). And this is only possible when the set in question has one-to-one correspondence with some subset of the set of natural numbers.

    What any of this has to do with the existence of the Christian God is beyond the scope of my response.

    Edit: Actually no, I think that Cantor himself had some weird idea that the absolute infinite is God. I know nothing further.

    Anyone feel free to correct me if I'm wrong on any point, as I am no practicing mathematician (just see my help with mathematical induction thread for proof positive).

    Edit Again: And actually, I was just going over BW's post again and noticed that he had several things wrong. One is the part quoted by dissonance about finite sets being defined as having a one-one relationship with the set of natural numbers. This is not true. A finite set is simply one whose cardinal number is a natural number (including zero). This is intuitively understandable because the cardinal number of a finite set is simply the number of members included in the set.
    Artes, Scientia, Veritasiness

  2. #182
    Occasional Member Evan's Avatar
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    Quote Originally Posted by Nocapszy View Post
    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.
    The numbers they divide to find those decimal places cannot both be expressed as fractions themselves at the same time...

  3. #183
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by Nocapszy View Post
    Er... except that it can be written as a fration, and it would would be an infinite number of digits not an infinite value -- it doesn't mean that the quantity continues to grow...

    And yet you didn't draw an ellipsis before the 1. .
    A number that cannot be written as a fraction is called an irrational. As an opposite of rational, which means could be written in a ratio or a fraction.

    If for example, in 3.6777777 the 7 goes on without an end, there cannot be a fraction because there are too many numbers to represent.



    Quote Originally Posted by Nocapszy View Post
    Out of curiosity, what comes before 1? What comes before that?
    Or did you accidentally prove my point that you can have one end and still be infinite? As long as there isn't a second end, it's still infinite. Unless you want to get into semi-finite, which I doubt, being against shades of gray as you are.

    The fact that there is one end, it is not completely infinite. It is, as I argued before is finite, unless an entity is completely boundless. For the sake of simplicity, only the completely boundless entities ought to be regarded as infinite. As boundlessness is the quintissence of infinity, and the defining quality of finitude is having limits.

    Quote Originally Posted by Nocapszy View Post
    .don't know what you're talking about. You've not only misapplied terms, but have breached appropriate context and interpreted patterns incorrectly.
    What term has been misapplied and how?

    Quote Originally Posted by Nocapszy View Post
    . If that's so, why didn't you say that in the beginning? Why use the synonym to convey a concept which is more accurately described using the other word? .
    This is quite obvious from the conventional definition of the term, needed no explanation.

    Quote Originally Posted by Nocapszy View Post
    .Know what? I'm not even going to wait for you to walk into that trap. You did it because english semantics and sentence structure doesn't allow you to. It would sound senseless to write that way. So instead, you have to revise the sentence inserting new words and removing the ones that don't fit your position. This lexicon displacement provides illusory proof..
    You're a tough kiddo nocap, I already know! No need to attempt to prove this to me. Very entertaining Ne bounces, unfortunately this isnt philosophy, but with some careful revision may pass for some good philosophical poetry. Hint: try bringing some structure to your thinking, its back to being all over the place, alas, you seem to have been improving in your previous short post.

    Quote Originally Posted by Nocapszy View Post
    .It means having a limit, while still not being really truly confined. We have a starting point, but no ending point. Who says you can't? You do. You're the only one, and you have no reason to say so...
    An entity that has any restrictions is not completely infinite, as aforementioned in this post. You know all this, and I need not explain it to you again.


    Quote Originally Posted by Nocapszy View Post
    . In fact I can. We call them black holes. Endless gravitational strengthc ...
    That is interesting indeed. Since they have no end, they must merge with the completely infinite entity outside of our universe. However, as far as human knowledge is concerned, they are just like the infinite set of natural numbers. We just know they have a beginning, and must progress infinitely, but we do not know exactly how they will progress infinitely as we cannot see where the end of our series will end. As we simply do not have enough room in our finite universe. Hence, from the standpoint of our understanding, because blackholes have a beginning, as far as we are concerned they have an end, past which we are unable to see. Yet for the purpose of greatest mathematical precision, it must be noted that this entity is indeed infinite. This is why in our notes we only mark that the natural set is infinite, but never bother to write out each member of the set individually. Will never have enough paper. Lets see if we can think of something that has no beginning, but has an end.

    Quote Originally Posted by Nocapszy View Post
    . Your turn -- I've asked for this more than once, and you've not done it.
    It has a beginning, but it doesn't have an end. Read up on black holes. They're really neato! ...
    I don't see the relevance?





    Quote Originally Posted by Nocapszy View Post
    . Incorrect. If this was the case, there would be no need for a ray, in mathematics. The concept would prove utterly useless, and therefore wouldn't be used ever, and maybe not even invented.
    The ray is an example of what you called the 'semi-finite'.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

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  4. #184
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by dissonance View Post
    Actually that number can be written in fraction form..
    No, it cannot be, as the 7 goes on infinitely. The same is the case with all the 'irrational numbers'.



    Quote Originally Posted by dissonance View Post
    Yes, a set that has finite length is finite...



    Quote Originally Posted by dissonance View Post
    No. You just quoted the definition. Countable means one to one correspondence with the natural numbers (which is an infinite set)...
    The only reason there would not be such a correspondence is if the value would be much too high for this.




    Quote Originally Posted by dissonance View Post
    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.)...
    Where is the difference between this and what I said?



    Quote Originally Posted by dissonance View Post
    @Bolded statement -- Nope..)...
    You have provided no reason to think otherwise. You know just like when you see small children playing in the sandbox, one of them tries to take the toy of the other, and the child clings to the toy and just screams and starts crying 'NOOOO!!!!!!!!'. Why not? The other child asks. He carries on 'NOOOOOOOO!"


    Quote Originally Posted by dissonance View Post
    @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.
    How is this different from being a very large set????? If it can be counted, we can see how large it is. The only difference in this case between an infinite set and a finite is size. If a set is uncountable, there would not be a one to one correspondence, and that'd be the classical case of the 'infinite' or what Rodgers called the 'higher levels of infinity'. The complete infinity would cover all things.

    Quote Originally Posted by Nocapszy View Post
    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.

    You have a stance? (Maybe 4 or 5 of them and no more than 1, if that is coherent) Really? Why dont you recapitulate it for me. Lets see if its still alive in your conscious bank of knowledge.

    .
    Quote Originally Posted by Orangey View Post
    A finite set is simply one whose cardinal number is a natural number (including zero). This is intuitively understandable because the cardinal number of a finite set is simply the number of members included in the set.
    So a finite set is one that is connected with any natural number. For instance, 4,5, or 6. What is the difference between this an the one to one correspondence?
    "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. #185
    Senior Member Bella's Avatar
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    Oh, hi guyyyyyyyyyyyyys!!!! You want to watch Pride and Prejudice with me?? Pleaaaaaaaaaase. Mr Darcy is sooooo wonderful. And Elizabeth Bennet.....OH. MY. WORD!
    When she walks through the tall grass......reading a book....I want to be JUST. LIKE. HER!!! Ooooooooh and those dresses! Why don't we dress like that anymore! Huh, guys.
    You wanna watch? Huh?
    I'll make crumpeeeeeets!
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    It's Mizzz ST, thank you...

  6. #186
    Tenured roisterer SolitaryWalker's Avatar
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    Quote Originally Posted by dissonance View Post
    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...
    There is only one possible dimension, and that is space. Time is only the way human mind incepts space. For example, time organizes how space appears to the human mind. If the human mind was completely infinite, the space would appear all at once. It would not need to be broken down into segments. Thus, time represents the finitude of our mind, as this is what shows that we cannot incept all things simultaneously.

    Also, if something is completely infinite, it occupies all things, which means all dimensions. If it does not occupy all things or all dimensions, it has restrictions, therefore is not completely infinite.



    He must be talking about a four dimensional (3 directional dimensions AND time) infinite. Or an infinite in space-time, I guess you could call it..

    Quote Originally Posted by dissonance View Post
    He's only been talking about an infinite in time, though, which need not take up any point in 3dimensional space.
    The only external or objective entity is space, the rest, including time are subjective or inhere within human perception. So, I am talking about space, which if infinite, occupies all things.
    "Do not argue with an idiot. They drag you down to their level and beat you with experience." -- Mark Twain

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  7. #187
    Occasional Member Evan's Avatar
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    Quote Originally Posted by BlueWing View Post
    No, it cannot be, as the 7 goes on infinitely. The same is the case with all the 'irrational numbers'.
    The number can be expressed as 331/90.

    AKA you are wrong. In fact, I'm slightly embarrassed even correcting you, since you obviously have no sense of math.

    An easier example is 1/3. In decimal notation, that is .3333333(to infinity). Are you saying 1/3 is not a fraction?

    The only reason there would not be such a correspondence is if the value would be much too high for this.
    What? A countable set is one of two things --
    a) A set with a finite length
    b) An infinite set with a one to one correspondence with the counting numbers. The set of counting numbers is not [1, 2, 3, 4, 5] or [1, 2, 3, 4, 5, 6, 7]. It is the set [1, 2, 3, 4, 5, 6, 7, ... (to infinity)]. It is an INFINITE SET. But it is countable.

    Jeez, how many times do I have to say this?

    Where is the difference between this and what I said?
    You said that it is countable because it is finite. That is not true.

    You have provided no reason to think otherwise. You know just like when you see small children playing in the sandbox, one of them tries to take the toy of the other, and the child clings to the toy and just screams and starts crying 'NOOOO!!!!!!!!'. Why not? The other child asks. He carries on 'NOOOOOOOO!"
    Well, if you actually read my words, I provided a definition that you have violated.

    No need to get all F on me.

    How is this different from being a very large set????? If it can be counted, we can see how large it is. The only difference in this case between an infinite set and a finite is size. If a set is uncountable, there would not be a one to one correspondence, and that'd be the classical case of the 'infinite' or what Rodgers called the 'higher levels of infinity'. The complete infinity would cover all things.
    Countable does not mean you can literally count it. It means one of two things: you can actually count it OR it is infinite and has a one to one correspondence to the infinite set of counting numbers.

    You have a stance? (Maybe 4 or 5 of them and no more than 1, if that is coherent) Really? Why dont you recapitulate it for me. Lets see if its still alive in your conscious bank of knowledge.
    How about reading what I've written? If it's too hard for you to understand, I don't see how that's my problem. I guess it shows your intellectual limits...

    Too bad. I don't want to have to say this, but I am literally a math genius. I've taken a real IQ test administered by a trained psychologist. You obviously aren't.

    So a finite set is one that is connected with any natural number. For instance, 4,5, or 6. What is the difference between this an the one to one correspondence?
    Wow dude, way to completely disregard everything I've said.

  8. #188
    Senior Member reason's Avatar
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    dissonance,

    It's easier to define countable sets as something like the following.

    A set is countable if its members have a 1 to 1 correspondence with a subset of the set of natural numbers.

    Thus a countable set can be finite or infinite, but cannot have a cardinal number greater than the set of natural numbers i.e. aleph naught.
    A criticism that can be brought against everything ought not to be brought against anything.

  9. #189
    Occasional Member Evan's Avatar
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    Quote Originally Posted by BlueWing View Post
    There is only one possible dimension, and that is space. Time is only the way human mind incepts space. For example, time organizes how space appears to the human mind. If the human mind was completely infinite, the space would appear all at once. It would not need to be broken down into segments. Thus, time represents the finitude of our mind, as this is what shows that we cannot incept all things simultaneously.
    Well, if you want to use a word 'dimension' that means something different than the definition everyone else uses, I guess you are right. You can't expect people to know what you're talking about though.

    Also, if something is completely infinite, it occupies all things, which means all dimensions. If it does not occupy all things or all dimensions, it has restrictions, therefore is not completely infinite.
    Ah. So you have defined "completely infinite" to mean infinite in all dimensions. No way anyone could have read your mind and figured this out, as it isn't how the terms are used by anyone in the academic world.

    The only external or objective entity is space, the rest, including time are subjective or inhere within human perception. So, I am talking about space, which if infinite, occupies all things.
    Oh, so there are things about the human experience which are not subjective? Interesting. I'd like to hear you back that one up.

    Everything we say is within the subjective human bubble. When talking, we implicitly accept this. Your argument can be made for anything, so it's essentially pointless.

  10. #190
    Occasional Member Evan's Avatar
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    Quote Originally Posted by reason View Post
    dissonance,

    It's easier to define countable sets as something like the following.

    Countable - a set is countable if its members have a 1 to 1 correspondence with a subset of the set of natural numbers.
    Actually, that definition is wrong. Infinite sets can be countable as long as they have a one to one correspondence with the ENTIRE infinite set of counting numbers.

    An example of an infinite countable set is [1, 4, 9, 16, 25, 36, ...(to infinity)] because it corresponds to the counting numbers by squaring each term.

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