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Alex
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Re: There is no God.

Postby Alex » Wed Jan 14, 2009 10:24 pm

There are no different infinities


You are wrong:
http://en.wikipedia.org/wiki/Cardinalit ... _continuum

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Thanatos
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Re: There is no God.

Postby Thanatos » Thu Jan 15, 2009 8:59 am

Wow, now even Alex has spoken up. Ayiyiyi...

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paul_one
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Re: There is no God.

Postby paul_one » Thu Jan 15, 2009 10:58 pm

Oh Alex... You're going onto "sets" of numbers.

That's just like saying that an infinite gibonacci sequence is larger or smaller than an infinite prime number sequence...
Or an infinite odd-number sequence is larger then an infinite integer/real number.

It's simply not-true, since neither are "countable".

I've looked through a few of those wiki pages - to tell you the truth most of that goes over my head since I don't know some of the basics that is grounded on.
BUT, they do not deal with the comparisons between them.

They rely on one being "countable" - which is not possible - and one being uncountable.
Defining one as "countable" because you can sort of get an "infinity/2" point in the middle (which you can't, since inf/2 is STILL infinity).
And the other based on the first _flawed_ assumption that infinity IS countable, and then saying "well wait, seeing as how we can have an infinite pattern of numbers, and that we can construct another infinite pattern different from the first, it's not possible to create a pattern, and we go on for infinity, we can't create one that's outside this set, so it's uncountable".

Defining "sets" or "ranges" for infinity is stupid, as the very definition is "unbounded". There is no end to the range.

Please, if anyone can produce GOOD proof, then please go ahead.

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Re: There is no God.

Postby Freak » Thu Jan 15, 2009 11:26 pm

Actually, the fibonacci numbers and primes are both countable.

A set is defined as being countable if it is possible to form a bijection between that set and some subset of the integers.

The integers, rational numbers, and algebraic numbers are all countable sets. The real numbers are not.

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Thanatos
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Re: There is no God.

Postby Thanatos » Thu Jan 15, 2009 11:46 pm

I UNDERSTAND NOTHING.

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paul_one
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Re: There is no God.

Postby paul_one » Fri Jan 16, 2009 12:06 am

I'm guessing from my interpretation of things I've just read up on, a bijection is - for instance - 1, 2... because natural numbers cannot go between 1 and 2, therefore you cannot go any further.

While real numbers are slightly different:
0.1
0.2
0.11....

BUT, that still doesn't not mean one is MORE infinite then the other.

The basis of saying that is:
0.111
0.000
.. you can always then go to:
0.1111
.... then:
0.nnnnnnnnnn
into infinity.

BUT, you can do that with NATURAL numbers:
1
2
3
4
n
nnnnn
into, wait for it: infinity.

They are basically saying "one is MORE infinite then the other, because it is 2 dimensional"

From this interpretation of "infinite" - 'countable' means: "1..2...infinity" while "uncountable" means: "1.000..., 2.0000..., -> infinity.00000..."
That right?

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paul_one
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Re: There is no God.

Postby paul_one » Fri Jan 16, 2009 12:48 am

Sorry - I should have said this before:
I recognise that in the mathematics world, there lies _proof_ of different "infinities", although to me they are utter b***s since infinity is a subjective term.
IE, an infinite area is of course different to an infinite cube, or hypercube, or an infinite forum thread, or an infinite bank account (I wish I had one of THOSE).
.. BUT there are not different "types" of infinity since "infinity" is simply a definition of an "unlimited, never-ending" number.

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Re: There is no God.

Postby Freak » Fri Jan 16, 2009 3:07 am

A bijection between sets A and B is a way to pair off the elements between them such that each element of A is paired with exactly one element of B, and the reverse.

Two sets are defined to be of equal magnitude if it is possible to form a bijection between their elements.

Set A is defined as being larger than set B if is possible to form a bijection between the elements of B and some subset of A, but it is not possible to form a bijection between the elements of A and B.

A set is defined as being finite if it is empty or it is possible to form a bijection between its members and those of the set { 1, 2, ... N } for some natural number N.

A set is defined as being infinite if it is not finite.

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Elexxorine
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Re: There is no God.

Postby Elexxorine » Fri Jan 16, 2009 7:01 pm

You guys are right on the first infinity, being that for natural numbers, etc. This is called aleph-null. 2^aleph-null = aleph-one.

http://en.wikipedia.org/wiki/Aleph_number

I learnt this from my father who has PhD in physics. :) Lucky got such an awesome dad.

Aleph-one can be visualised like this:

1.59798046...
1.95369454...
1.37573033...
1.38066603...
1.17095437...
1.29848485...
1.52694954...
1.49497496...
... etc are are a set of numbers which are infinite (aleph-null). But we can make a new number by taking the diagonal of the decimals, like this:
1.55565456...
are there are infinite number of these from an infinite set, this is aleph-one.

Not explained very well, and been a long time since learning this then not using it for years.

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paul_one
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Re: There is no God.

Postby paul_one » Fri Jan 16, 2009 11:35 pm

That seems like a /slight/ mis-interpretation of the diagonal theorem..
Since in theory you could generate a number that has pre-existed.
The only way I see it truely working is in the limited scope of ordered binary sets... *shrugs*

BUT there you go, the only way to define differences in infinity (and actually, it isn't different 'infinities', it is in actuality different infinite 'sets') is in set theory - which is flawed IMO.

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Re: There is no God.

Postby METALGod32 » Sun Jan 18, 2009 6:41 am

What people fail to realize is that God is a meaning and a meaning only, God means Ruler or Creator, I'm
a big believer of Karma but I do believe in God to.

Alex is a God(in a weird way), God of Quest and this community.
I Believe that God of Life is nature, Nature is also the God of Death, since
both are natural.

I know that some will disagree but that's cool to, this is what makes us human.
Just because some do horrible acts to animals doesn't make it right to
hate humans, then your no better then them, I Love both, Animals and Humans.
Animal is NOT a bad word, just people make it sound bad, Animal and Humans have
different names because it's what we chose to call them.

I usually don't talk about religion and stuff, people usually get offended very easily.

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Thanatos
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Re: There is no God.

Postby Thanatos » Tue Jan 20, 2009 12:52 pm

Once upon a time we were talking about a puppy getting butchered :?

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Elexxorine
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Re: There is no God.

Postby Elexxorine » Tue Jan 20, 2009 12:58 pm

Yes, clearly Alex is god and this is his temple...

If I was to follow any religion it'd be Laveyan Satanism, which has satan as the concept not as a fawn-like creature. With rules like:
Do not give opinions or advice unless you are asked.
Do not tell your troubles to others unless you are sure they want to hear them.
When in another’s lair, show them respect or else do not go there.
If a guest in your lair annoys you, treat them cruelly and without mercy.
Do not make sexual advances unless you are given the mating signal.
Do not take that which does not belong to you, unless it is a burden to the other person and they cry out to be relieved.
Acknowledge the power of magic if you have employed it successfully to obtain your desires. If you deny the power of magic after having called upon it with success, you will lose all you have obtained.
Do not complain about anything to which you need not subject yourself.
Do not harm little children.
Do not kill non-human animals unless you are attacked or for your food.
When walking in open territory, bother no one. If someone bothers you, ask them to stop. If they do not stop, destroy them.
And sins such as:
Stupidity, Pretentiousness, Solipsism, Self-deceit, Herd Conformity, Lack of perspective, Forgetfulness of Past Orthodoxies, Counterproductive Pride, Lack of Aesthetics.
Some good rules to live buy and not really evil at all, and a hell of alot better than praying to some imaginary figure for wealth and fortune.

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Thanatos
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Re: There is no God.

Postby Thanatos » Tue Jan 20, 2009 1:05 pm

Agreed!

[LOCKED]

(I can dream, can't I?)

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Redsun
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Re: There is no God.

Postby Redsun » Tue Jan 20, 2009 2:23 pm

My father once told me a story, and it goes like this.

Along time ago many of the worlds top scientist got together to create what
they called a computer, this computer was as big as a building, the purpose of
this computer was to answer questions.

After completing the computer all of the scientist and leaders gathered around it.
They began to ask it questions, Like how old is the earth? a paper came out of
it's slot that said: 4.4 billion years old.
Back then there were no monitors.
Another person asked a question: are Humans different then animals?, the paper again came out, it
said: only now

One scientist decided to ask it the biggest question of them all!, is there a God?, after a delay the paper
came out and it said: There is now!.


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