My (infinite) Number is Bigger!

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My (infinite) Number is Bigger!

Postby darkspork » Sun Jun 06, 2010 4:43 pm UTC

As if the other thread wasn't confusing enough, in this thread the objective is to post an infinite number larger than the previous infinite number. Let's see how far this goes before I'm completely lost. Of course, note that adding one to the previous number, by the bizarre nature of infinity, will not make it any higher. No using previous definitions in your number. I'll start with:

The number of positive integers.
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Re: My (infinite) Number is Bigger!

Postby coolguy5678 » Sun Jun 06, 2010 5:16 pm UTC

The number of real numbers.

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Re: My (infinite) Number is Bigger!

Postby Gypped » Sun Jun 06, 2010 9:36 pm UTC

The number of entries in the power set of the set of complex numbers, which is [imath]\beth_2[/imath] I believe.

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Re: My (infinite) Number is Bigger!

Postby Welsh Mullet » Sun Jun 06, 2010 10:15 pm UTC

The number of decimal places in Pi

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Re: My (infinite) Number is Bigger!

Postby Nautilus » Sun Jun 06, 2010 10:54 pm UTC

The number of numbers in the set of quaternions.
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Re: My (infinite) Number is Bigger!

Postby eggdudeguy » Mon Jun 07, 2010 1:47 am UTC

The Finite Number thread defined finite numbers through ordinals, which are infinite numbers.

Thus, any of the ordinals we constructed there are eligible here...
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Re: My (infinite) Number is Bigger!

Postby itaibn » Mon Jun 07, 2010 3:16 am UTC

i
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Re: My (infinite) Number is Bigger!

Postby LucasBrown » Mon Jun 07, 2010 4:04 am UTC

Gypped wrote:The number of entries in the power set of the set of complex numbers, which is [imath]\beth_2[/imath] I believe.

Actually, it's [imath]\aleph_2[/imath].
That post is currently the winner. The number of decimal places in pi is just [imath]\aleph_0[/imath], the infinity of the integers, as is the number of numbers in the set of quaternions. And i is just... finite and puny.

As for my number, I'll call the number of functions in the x-y plane. I think that's [imath]\aleph_3[/imath]. If it's really just [imath]\aleph_2[/imath], then I'll call the number of entries in the power set of the set of those functions, which would then be [imath]\aleph_3[/imath].

We could just blow all this to meaningless bits by calling [imath]\aleph_{\aleph_{\aleph_{\aleph_{\aleph_{\aleph_{\aleph_{\aleph_{\aleph_{_{._{._{._{0}}}}}}}}}}}}}[/imath].

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Re: My (infinite) Number is Bigger!

Postby coolguy5678 » Mon Jun 07, 2010 1:21 pm UTC

I'm going to go with aleph-xkcd, where xkcd is of course A(g_64, g_64).

Or is that not fun?

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Re: My (infinite) Number is Bigger!

Postby eggdudeguy » Mon Jun 07, 2010 3:33 pm UTC

eggdudeguy wrote:The Finite Number thread defined finite numbers through ordinals, which are infinite numbers.

Thus, any of the ordinals we constructed there are eligible here...


Λ is the suprenum of {[imath]\aleph_0, \aleph_{\aleph_0}, \aleph_{\aleph_{\aleph_0}}, \cdots[/imath]}, and is now the "largest" number in this thread.

If we have some sort of restriction on needing a more "physical" basis for our infinite numbers, such as "number of all possible curves" (א2), then it's still meaningless because you can call

the number of natural numbers, {0, 1, 2, 3, 4, 5, ...}
the total amount of numbers in a set where each entry has every real number, {{0, 1, 2, 3, 4, 5, ...}, {0, 1, 2, 3, 4, 5, ...}, {0, 1, 2, 3, 4, 5, ...}, ...}
the total amount of numbers in a set where each entry is the previous set, {{{0, 1, 2, 3, 4, 5, ...}, {0, 1, 2, 3, 4, 5, ...}, {0, 1, 2, 3, 4, 5, ...}, ...}, {{0, 1, 2, 3, 4, 5, ...}, {0, 1, 2, 3, 4, 5, ...}, {0, 1, 2, 3, 4, 5, ...}, ...}, ...}
do this for an infinite amount of iterations, and your final result should be [imath]\aleph_{\aleph_0}[/imath], I believe.
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Re: My (infinite) Number is Bigger!

Postby itaibn » Mon Jun 07, 2010 9:23 pm UTC

The smallest cardinal [imath]\kappa[/imath] such that [imath]V_\kappa[/imath] is a model of ZFC (note: this is not an inaccessible cardinal).
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Re: My (infinite) Number is Bigger!

Postby Kromix » Mon Jun 07, 2010 9:26 pm UTC

WHATEVER HE SAID PLUS 1, IN ALL CAPS!!!11ONWEONEONE
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Re: My (infinite) Number is Bigger!

Postby Tillian » Mon Jun 07, 2010 9:47 pm UTC

coolguy5678 wrote:Or is that not fun?
Correct.
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Re: My (infinite) Number is Bigger!

Postby darkspork » Tue Jun 08, 2010 12:01 am UTC

My God, what have I done?
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Re: My (infinite) Number is Bigger!

Postby Kromix » Tue Jun 08, 2010 1:00 am UTC

hold on, i'm dividing by zero :twisted:
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Re: My (infinite) Number is Bigger!

Postby darkspork » Thu Jun 10, 2010 12:13 am UTC

Kromix wrote:hold on, i'm dividing by zero :twisted:

But that's not infinite! That's *gasp* UNDEFINED
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Re: My (infinite) Number is Bigger!

Postby WillyG » Thu Jun 10, 2010 3:37 am UTC

π to the power of π squared.

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Re: My (infinite) Number is Bigger!

Postby coolguy5678 » Thu Jun 10, 2010 10:07 am UTC

itaibn wrote:The smallest cardinal [imath]\kappa[/imath] such that [imath]V_\kappa[/imath] is a model of ZFC (note: this is not an inaccessible cardinal).
And we are now out of my knowledge of maths. Oh well, was fun while it lasted.

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Re: My (infinite) Number is Bigger!

Postby darkspork » Fri Jun 11, 2010 4:44 pm UTC

WillyG wrote:π to the power of π squared.

Not even remotely close
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Re: My (infinite) Number is Bigger!

Postby Mishrak » Fri Jun 11, 2010 8:50 pm UTC

The improbability of a whale and a pot of flowers materializing out of thin air in deep space. Also extremely far out of my knowledge of math :P

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Re: My (infinite) Number is Bigger!

Postby WarDaft » Sat Jun 12, 2010 4:14 am UTC

Mishrak wrote:The improbability of a whale and a pot of flowers materializing out of thin air in deep space. Also extremely far out of my knowledge of math :P

Finite, and thus, easily beaten.

Unfortunately, there is rather a way to "sort of" win this, because the largest cardinals rely on properties that can't be easily surpassed in a non-trivial way... and there is in fact a list of such massive cardinals on Wikipedia.
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Re: My (infinite) Number is Bigger!

Postby darkspork » Sun Jun 13, 2010 5:46 am UTC

How about the sum of all non-negative numbers? I seriously don't think it's possible to describe a larger infinity.
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Re: My (infinite) Number is Bigger!

Postby WarDaft » Sun Jun 13, 2010 5:56 am UTC

darkspork wrote:How about the sum of all non-negative numbers? I seriously don't think it's possible to describe a larger infinity.

You can't describe that infinity either if you meant it as including all infinite numbers as well. =p
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Re: My (infinite) Number is Bigger!

Postby darkspork » Sun Jun 13, 2010 6:02 am UTC

WarDaft wrote:
darkspork wrote:How about the sum of all non-negative numbers? I seriously don't think it's possible to describe a larger infinity.

You can't describe that infinity either if you meant it as including all infinite numbers as well. =p

I suppose. The interesting thing is that this definition, should it include all infinite numbers as well, would cause it to be greater than every conceivable number including itself. Does that make it impossible? Gah. Infinity hurts to think about.
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Re: My (infinite) Number is Bigger!

Postby WarDaft » Sun Jun 13, 2010 8:17 am UTC

darkspork wrote:
WarDaft wrote:
darkspork wrote:How about the sum of all non-negative numbers? I seriously don't think it's possible to describe a larger infinity.

You can't describe that infinity either if you meant it as including all infinite numbers as well. =p

I suppose. The interesting thing is that this definition, should it include all infinite numbers as well, would cause it to be greater than every conceivable number including itself. Does that make it impossible? Gah. Infinity hurts to think about.

Actually, considering how summing cardinality works, it would just be equal to the "largest" cardinal number, which is a well known paradox.
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Re: My (infinite) Number is Bigger!

Postby eggdudeguy » Sun Jun 13, 2010 7:56 pm UTC

Georg Cantor did conceive the idea of an absolute infinity...
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Re: My (infinite) Number is Bigger!

Postby snowyowl » Mon Jun 14, 2010 1:50 am UTC

The smallest number which is strictly larger than every other number posted on this thread.
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Re: My (infinite) Number is Bigger!

Postby Josephine » Mon Jun 14, 2010 1:58 am UTC

snowyowl wrote:The smallest number which is strictly larger than every other number posted on this thread.


darkspork wrote:No using previous definitions in your number.
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Re: My (infinite) Number is Bigger!

Postby snowyowl » Mon Jun 14, 2010 2:32 am UTC

Fine.

The smallest infinite number which is strictly larger than every number other than itself.

Or 1 if there is no such number (in which case, I will go down without regrets)
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Re: My (infinite) Number is Bigger!

Postby WarDaft » Mon Jun 14, 2010 7:32 am UTC

snowyowl wrote:Fine.

The smallest infinite number which is strictly larger than every number other than itself.

Or 1 if there is no such number (in which case, I will go down without regrets)

Suppose K is that number.

K contends that K > PowerSet(K) - the infinite equivalent of asking for some n > 2^n.
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Re: My (infinite) Number is Bigger!

Postby snowyowl » Mon Jun 14, 2010 10:33 am UTC

Okay, so I guess that means my entry is 1 then. I'll stop toying with forces I don't understand. Sorry.
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Re: My (infinite) Number is Bigger!

Postby black_hat_guy » Sun Nov 14, 2010 5:34 am UTC

The number of mathematical objects.
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Re: My (infinite) Number is Bigger!

Postby xkcdfan » Wed Dec 01, 2010 2:56 pm UTC

.........999999999

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Re: My (infinite) Number is Bigger!

Postby GenericPseudonym » Thu Dec 02, 2010 5:04 am UTC

How about... [imath]\aleph_\omega[/imath]?

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Re: My (infinite) Number is Bigger!

Postby WarDaft » Thu Dec 02, 2010 7:37 am UTC

Let us generalize the notion of a set and classes to a hierarchy.

Specifically, let's rename the empty set from {} to {}0, then, we will call a set satisfactorily defined in this hierarchy if it satisfies the traditional requirements of a well defined finite or infinite set, and furthermore, ∀Bb∈Aa(b ≤ a). In this manner, the {...}0 sets will be all the regular sets, then we can imagine a set B1 as the set of all sets A0, or the class of all sets. We could then have a C2 as a megaclass of all classes. But really, this doesn't get us all that far in the grand scheme of things.

Instead, let's write ∀Bb∈Aa(b ⊆ a). To top it off we'll have K be the class of all well defined sets in this extended system.
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Re: My (infinite) Number is Bigger!

Postby Boreeas » Sun Dec 12, 2010 3:39 am UTC

The number of multiples of the smallest number greater than 1.

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Re: My (infinite) Number is Bigger!

Postby eggdudeguy » Sun Dec 12, 2010 8:08 am UTC

I've been thinking about this thread and I wondered -- what about the total number of possible worlds?
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Re: My (infinite) Number is Bigger!

Postby WarDaft » Sun Dec 12, 2010 9:50 am UTC

That depends on how much of math is something you get to decide versus something that simply produces a contradiction if you chose wrong. Either A) It's not very big because almost all statements just produce a contradiction, or B) It's arbitrarily big and thus ill-defined.

If we're talking about empirical possibilities, then there's no evidence that it's larger even than [imath]\beth_2[/imath]
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