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Set Theory
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dolio
Royal Citizen

Joined: 31 Jul 2005
Posts: 457
Local time: 8:02 AM

Posted: Mon Sep 29, 2008 11:43 pm Post subject:

abstract atheist wrote:

Wait, let me get this straight. You are saying that Q is a set of sets of naturals, like:
Q={ {1,2,3,4,5,6,7} , {5433, 4554, 5454} , {1,2,3,4}}
But each set of natural numbers is itself associated with a natural number:
Q={8,10,5}
But Q is now a set of natural numbers, so it is a natural number:
Q=1
Is that what you are saying?

If you accept the (ultimately contradictory) premises of the argument, yes:

Quote:

1. Any infinite set is enumerable if and only if it is equinumerous with the set of positive integers (I can prove this if you want, but for brevity, I won't. The proof is quite simple).
2.Assume for contradiction R = P+.
3. If this is true, then there is a function from the real numbers to the set of positive integers such that the function is total, onto and equinumerous.
4. What this means is that every element a in R is mapped to some element b in P+, that every element in P+ is defined for some a in R and that no element a in R is assigned to no more than one element of b in P+.
5.Now, by definition, R = P(N). P(N) = the set of all subsets of natural numbers. By assumption, we are assuming R = P+, which defines a function which has the property of equinumerousity.

{8, 10, 5} is not a natural number, but it has been associated with a unique natural number. So if you have a set of sets of natural numbers, Q, it is obviously related to a unique set of natural numbers, which is itself related to a unique natural number.

Dragonfall
Intern
Intern

Joined: 08 Apr 2007
Posts: 53
Local time: 8:02 AM

Posted: Mon Sep 29, 2008 11:43 pm Post subject:

Dragonfall wrote:

Wait, wait, something's not right here. omega^omega is not countable. That picture is making it look like it is.

My bad. I was confusing ordinal exponentiation with cardinal exponentiation.

Raskolnikov
The Axe Murderer

Joined: 22 Oct 2007
Posts: 2072
Local time: 6:02 AM
Location: Las Vegas

Posted: Mon Oct 06, 2008 9:18 pm Post subject:

Raskolnikov wrote:

Chaoslord2004 wrote:

Moloth wrote:

Chaoslord2004 wrote:

Moloth wrote:

heh.. this reminds of that "mathematicians that have gone crazy" video. once you realize that, not only that infinity exists... but that there are an infinite NUMBER of them... its a little.. brain melting. >_O

But thats what so awesome and beautiful about it. It stretches the limits of what is even thinkable. It isn't easy to wrap your head around an infinite hierarchy of infinities...and thats why I like it.

its concept like this that i wonder if sentient minds will EVER be able to 'really' comprehend... even with genetic or technological enhancement.

Nope. Take the set of real numbers (the rational and irrational numbers). These numbers are uncountably infinite, as are all the higher order infinities. God, if he existed, couldn't count them. If he could apprehend them, he could put them into one-to-one correspondence with the positive integers. But, as Cantor showed, this is a contradiction. All infinities beyond the carnality of the positive integers are to big for ANYONE...or thing, to ever grasp entirely.

Hmm... This gives me an idea:

If God can do anything can he count to infinity?

Can anyone tell me if my question is tenable? I want to make sure lol
_________________
"Shake off all the fears of servile prejudices, underwhich weak minds are servilely crouched. Fix reason firmly in her seat and call on her tribunal for every fact, every opinion. Question with boldness even the existence of a God, for if there be one, he must more approve of the homage of reason, than that of blindfolded fear."
-Thomas Jefferson

"The future is not set in stone. The future is what you make it. So make it a good one!"
-Dr. Emmett Brown

Raskolnikov
The Axe Murderer

Joined: 22 Oct 2007
Posts: 2072
Local time: 6:02 AM
Location: Las Vegas

Posted: Tue Oct 07, 2008 12:11 am Post subject:

Raskolnikov wrote:

Chaoslord2004 wrote:

Moloth wrote:

Chaoslord2004 wrote:

Moloth wrote:

its concept like this that i wonder if sentient minds will EVER be able to 'really' comprehend... even with genetic or technological enhancement.

Hmm... This gives me an idea:

If God can do anything can he count to infinity?

Can anyone tell me if my question is tenable? I want to make sure lol

no one?...
_________________
"Shake off all the fears of servile prejudices, underwhich weak minds are servilely crouched. Fix reason firmly in her seat and call on her tribunal for every fact, every opinion. Question with boldness even the existence of a God, for if there be one, he must more approve of the homage of reason, than that of blindfolded fear."
-Thomas Jefferson

"The future is not set in stone. The future is what you make it. So make it a good one!"
-Dr. Emmett Brown

Moloth
Fateless

Joined: 27 Aug 2003
Posts: 23105
Local time: 8:02 AM
Location: Warner Robins, GA

Posted: Tue Oct 07, 2008 8:51 am Post subject:

well.. considering you're on an atheist forum.. you might have to wait a while before getting an answer... lol.. just sayn'. _________________ -=The Believer is Happy; the Skeptic is Wise=- www.Moloth.com Last edited by Moloth on Tue Feb 30, 2026 13:61 am; edited 426 times in total

abstract atheist
Forum Leader

Joined: 02 Sep 2008
Posts: 607
Local time: 8:02 AM
Location: Austin, Texas

Posted: Thu Oct 09, 2008 11:07 pm Post subject:

Raskolnikov wrote:

Chaoslord2004 wrote:

Moloth wrote:

Chaoslord2004 wrote:

Moloth wrote:

its concept like this that i wonder if sentient minds will EVER be able to 'really' comprehend... even with genetic or technological enhancement.

Hmm... This gives me an idea:

If God can do anything can he count to infinity?

Can anyone tell me if my question is tenable? I want to make sure lol

no one?...

No, god cannot count to infinity. There is no infinity to count to. God cannot count the real numbers either. He also cannot make a fraction (made of integers) equal the square root of 2. He cannot find an elementary function whose derivative is e^{x^2}. Mathematics puts restrictions on everything, even god, if he existed.
_________________
MAN: Jesus, how do I get to heaven?
JESUS: Give up all of your knowledge, and follow me. For blessed are the ignorant, for theirs the kingdom of heaven.
MAN: But I like knowledge.
JESUS: But I prepared hell for people who ask question and think for themselves. You must blindly follow me with child like faith.
MAN: That sucks.
JESUS: Also, cut your penis off. I want to make sure you don't enjoy ANYTHING. It is better for a man to lose his penis, than have his whole body cast into hell.

Raskolnikov
The Axe Murderer

Joined: 22 Oct 2007
Posts: 2072
Local time: 6:02 AM
Location: Las Vegas

Posted: Fri Oct 10, 2008 12:26 am Post subject:

abstract atheist wrote:

Raskolnikov wrote:

Chaoslord2004 wrote:

Moloth wrote:

Chaoslord2004 wrote:

Moloth wrote:

its concept like this that i wonder if sentient minds will EVER be able to 'really' comprehend... even with genetic or technological enhancement.

Hmm... This gives me an idea:

If God can do anything can he count to infinity?

Can anyone tell me if my question is tenable? I want to make sure lol

no one?...

All right, thank you. I'll just add these to my arsenal heheh.
_________________
"Shake off all the fears of servile prejudices, underwhich weak minds are servilely crouched. Fix reason firmly in her seat and call on her tribunal for every fact, every opinion. Question with boldness even the existence of a God, for if there be one, he must more approve of the homage of reason, than that of blindfolded fear."
-Thomas Jefferson

"The future is not set in stone. The future is what you make it. So make it a good one!"
-Dr. Emmett Brown

abstract atheist
Forum Leader

Joined: 02 Sep 2008
Posts: 607
Local time: 8:02 AM
Location: Austin, Texas

Posted: Fri Oct 10, 2008 8:30 am Post subject:

Raskolnikov wrote:

abstract atheist wrote:

Raskolnikov wrote:

Chaoslord2004 wrote:

Moloth wrote:

Chaoslord2004 wrote:

Moloth wrote:

its concept like this that i wonder if sentient minds will EVER be able to 'really' comprehend... even with genetic or technological enhancement.

Hmm... This gives me an idea:

If God can do anything can he count to infinity?

Can anyone tell me if my question is tenable? I want to make sure lol

no one?...

All right, thank you. I'll just add these to my arsenal heheh.

The funny thing is that the Christian god already has restrictions placed on him. He cannot sin, for example. But he defined what sin was, and he made the rule that he cannot sin, so he put restrictions on himself. In fact, if you look at it like this it is manifestly insane.
1. God made a list of actions that he defined as sin.
2. God made the rule that he cannot sin.
3. God made the rule that if you sin, you will burn in hell forever and ever and ever. He also made the rule that if you sin, your descendents will sin, and they will have to burn in hell forever and ever.
4. Oops, somebody sinned.
5. God was sorry that he made such stupid rules.
6. Somehow killing himself on a cross nulls the above rules.
_________________
MAN: Jesus, how do I get to heaven?
JESUS: Give up all of your knowledge, and follow me. For blessed are the ignorant, for theirs the kingdom of heaven.
MAN: But I like knowledge.
JESUS: But I prepared hell for people who ask question and think for themselves. You must blindly follow me with child like faith.
MAN: That sucks.
JESUS: Also, cut your penis off. I want to make sure you don't enjoy ANYTHING. It is better for a man to lose his penis, than have his whole body cast into hell.

josephpalazzo
Illusion Master

Joined: 30 Aug 2006
Posts: 8036
Local time: 8:02 AM
Location: D-brane

Posted: Fri Oct 10, 2008 9:14 am Post subject:

Number 6 is insane, absurd and ridiculous... come to think of it... I like it...

abstract atheist
Forum Leader

Joined: 02 Sep 2008
Posts: 607
Local time: 8:02 AM
Location: Austin, Texas

Posted: Fri Oct 10, 2008 12:31 pm Post subject:

josephpalazzo wrote:

Number 6 is insane, absurd and ridiculous... come to think of it... I like it... Snakeman

When I was a kid, they told us about the cross story, but didn't tell us why. So I had to come up with my own justification. It went something like this:
1. Sin is a physical thing. There is a sin field and corresponding quanta known as the sin boson.
2. When God created the world, the sin field was in the vacuum state.
3. God placed a sin creation operator in the forbidden fruit of the tree of knowledge.
4. When they ate the fruit, they were actually apllying the sin creation operator to the vacuum, creating sin bosons.
5. The sin annihilation operator was in hell. God had to somehow get from heaven to hell, get the annihilation operator, and apply it to the sin field a bunch of times to eliminate the sin from the universe. The reason is clear: God cannot look at sin, and since humans were stained with sin bosons, they could not enter heaven until all the sin bosons in their souls were annihilated.
6. so god came to earth, died, and went to hell. Just before he died, he absorbed all the sin bosons in the entire universe, past, present, and future.
7. When he was in hell, he took the sin bosons and the annihilation operator, and annihilated them.
8. Now we can all go to heaven, sin free.
This is my PhD thesis in a nutshell.
_________________
MAN: Jesus, how do I get to heaven?
JESUS: Give up all of your knowledge, and follow me. For blessed are the ignorant, for theirs the kingdom of heaven.
MAN: But I like knowledge.
JESUS: But I prepared hell for people who ask question and think for themselves. You must blindly follow me with child like faith.
MAN: That sucks.
JESUS: Also, cut your penis off. I want to make sure you don't enjoy ANYTHING. It is better for a man to lose his penis, than have his whole body cast into hell.

kmisho
Stochastic

Joined: 05 Dec 2005
Posts: 4811
Local time: 11:02 PM
Location: Richmond, Virginia USA

Posted: Fri Oct 10, 2008 12:39 pm Post subject:

Classic infinity paradoxes... God can count to infinity, because he has the ability to count infinitely fast. _________________ K Michau Now this religion happens to prevail/Until by that one it is overthrown/Because men dare not live with men alone/But always with another fairy tale. al-Ma'arri, Syrian Poet, died 1057 You deny the existence of 999 alleged Gods. I merely deny one more - yours. John MacKinnon Robertson, "Godism" 1896 "Never is a long time." Robert Fripp, 1998 Poetry, Art, Music

josephpalazzo
Illusion Master

Joined: 30 Aug 2006
Posts: 8036
Local time: 8:02 AM
Location: D-brane

Posted: Fri Oct 10, 2008 1:49 pm Post subject:

abstract atheist wrote:

josephpalazzo wrote:

Number 6 is insane, absurd and ridiculous... come to think of it... I like it... Snakeman

Lol. Another reason why PhD = Pile high and Deep

abstract atheist
Forum Leader

Joined: 02 Sep 2008
Posts: 607
Local time: 8:02 AM
Location: Austin, Texas

Posted: Fri Oct 10, 2008 2:39 pm Post subject:

josephpalazzo wrote:

abstract atheist wrote:

josephpalazzo wrote:

Number 6 is insane, absurd and ridiculous... come to think of it... I like it... Snakeman

Lol. Another reason why PhD = Pile high and Deep

Of course I'm kidding, but I am going to make a you tube video that states that, in a more thought out way. Unfortunately people will actually think that I believe this, but it's worth it.
_________________
MAN: Jesus, how do I get to heaven?
JESUS: Give up all of your knowledge, and follow me. For blessed are the ignorant, for theirs the kingdom of heaven.
MAN: But I like knowledge.
JESUS: But I prepared hell for people who ask question and think for themselves. You must blindly follow me with child like faith.
MAN: That sucks.
JESUS: Also, cut your penis off. I want to make sure you don't enjoy ANYTHING. It is better for a man to lose his penis, than have his whole body cast into hell.

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