## My (infinite) Number is Bigger!

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darkspork
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### My (infinite) Number is Bigger!

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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coolguy5678
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### Re: My (infinite) Number is Bigger!

The number of real numbers.

Gypped
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### Re: My (infinite) Number is Bigger!

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

Welsh Mullet
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### Re: My (infinite) Number is Bigger!

The number of decimal places in Pi

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### Re: My (infinite) Number is Bigger!

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

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!

i
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LucasBrown
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### Re: My (infinite) Number is Bigger!

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].

coolguy5678
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### Re: My (infinite) Number is Bigger!

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

Or is that not fun?

eggdudeguy
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### Re: My (infinite) Number is Bigger!

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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itaibn
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### Re: My (infinite) Number is Bigger!

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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Kromix
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### Re: My (infinite) Number is Bigger!

WHATEVER HE SAID PLUS 1, IN ALL CAPS!!!11ONWEONEONE

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Tillian
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### Re: My (infinite) Number is Bigger!

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

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

hold on, i'm dividing by zero

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darkspork
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### Re: My (infinite) Number is Bigger!

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

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

π to the power of π squared.

coolguy5678
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### Re: My (infinite) Number is Bigger!

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.

darkspork
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### Re: My (infinite) Number is Bigger!

WillyG wrote:π to the power of π squared.

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

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

WarDaft
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### Re: My (infinite) Number is Bigger!

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

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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darkspork
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### Re: My (infinite) Number is Bigger!

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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WarDaft
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### Re: My (infinite) Number is Bigger!

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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darkspork
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### Re: My (infinite) Number is Bigger!

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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WarDaft
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### Re: My (infinite) Number is Bigger!

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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eggdudeguy
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### Re: My (infinite) Number is Bigger!

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

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

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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snowyowl
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### Re: My (infinite) Number is Bigger!

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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WarDaft
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### Re: My (infinite) Number is Bigger!

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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snowyowl
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### Re: My (infinite) Number is Bigger!

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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black_hat_guy
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### Re: My (infinite) Number is Bigger!

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

.........999999999

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### Re: My (infinite) Number is Bigger!

WarDaft
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### Re: My (infinite) Number is Bigger!

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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Boreeas
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### Re: My (infinite) Number is Bigger!

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

eggdudeguy
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### Re: My (infinite) Number is Bigger!

KrazyerKate wrote:While it's probably the strangest sounding advice I will ever give, we need to stay focused on Hardcore Pornography in order to be successful.

I have a Blog and I make Games. I also have a big multiplayer game in the works (coming soonish!).

WarDaft
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### Re: My (infinite) Number is Bigger!

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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