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., alephnull). And this is only possible when the set in question has onetoone 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 oneone 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.
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Thread: Why I do not believe in God

09292008, 06:01 PM #181Artes, Scientia, Veritasiness

09292008, 06:02 PM #182

09292008, 10:24 PM #183
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.
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.
What term has been misapplied and how?
This is quite obvious from the conventional definition of the term, needed no explanation.
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.
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.
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.
I don't see the relevance?
The ray is an example of what you called the 'semifinite'."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/

09292008, 10:33 PM #184
No, it cannot be, as the 7 goes on infinitely. The same is the case with all the 'irrational numbers'.
The only reason there would not be such a correspondence is if the value would be much too high for this.
Where is the difference between this and what I said?
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!"
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.
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.
. 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
“No man but a blockhead ever wrote, except for money.”Samuel Johnson
My blog: www.randommeanderings123.blogspot.com/

09292008, 10:40 PM #185
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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!yesiknowimamiserablegrouchnowgoawayovmeleor
It's Mizzz ST, thank you...

09292008, 10:46 PM #186
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 spacetime, I guess you could call it..
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
“No man but a blockhead ever wrote, except for money.”Samuel Johnson
My blog: www.randommeanderings123.blogspot.com/

09292008, 11:50 PM #187
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.
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 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!"
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.
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.
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?

09292008, 11:55 PM #188
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.

09292008, 11:55 PM #189
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.
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.
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.

09292008, 11:59 PM #190
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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