if you want infinitely many things to come out of seemingly nothing, there are plenty mathematical constructs which can do that
eg there is a further extension of numbers beyond the complex ones, namely quaternions and there you get infinitely many square roots of -1
and btw, there are infinitely many different infinities which might be a little bit too godly for a proof of god

i was just expecting more then hey look i took these 5 constants and made something pretty.

the hotel thing?

let's leave it here, else we might be just be talking past each other again due to different understanding
but no, it's different to the hotel concept with shuffling the rooms around (assuming you refer to that)
[if i remember it right the hotel concept's infinity is still the simplest form of infinity - "Azrad" watching, he might be able to confirm]

just googled for it and this is what you are refering to i think: http://en.wikipedia.org/wiki/Hilberts%5Fparadox%5Fof%5Fthe%5FGrand%5FHotel
and yes, i remembered right, it is countable infinity which is the simplest form

This post was edited by brmv on May 3 2013 10:10am

i was just refering to the infinitely many different infinities, yes thats what i was talking about, though i guess thats more so infinate infintiies with in infinity.

This post was edited by Ylem122 on May 3 2013 10:15am

oh god

they're playing with infinites again

all the infinitely many grand hotels etc you can build still have the same infinity, namely the infinity shared with the natural numbers
if you take the power set of all natural numbers you get another 'level' of infinity
now you take the power set of any set having that new level of infinity and you get an even higher level of infinity
and so on and so on, so it's not another version of a specific 'level' of infinity but something genuinely different

hope you are not totally confused by this

That is pretty much it. It is a cool and useful identity (a true statement). No more so than Cos(x)^2 + Sin(x)^2 = 1 (imo).

The easiest way I know to derive it is to calculate the Maclaurin series of:
e^(ix)
sin(x)
cos(x)
and then Euler's formula will become obvious. Substitute x = pi and you get the identity quoted above. Of course as brmv eluded too, if you don't know what any of that means, well then you've got some work ahead of you.

as i finally found out in post#528 he wanted something to put his hands on, a real world equivalent
maybe i should have realised that earlier, so in some regard we were talking past each other
your comments are not really helpful for him, doubt he wants to go through that trouble
for me the most beautiful simple thing in maths is the plain moebius strip

each one according to the awakening of knowledge.
If you are happy to believe that way, we have to respect.
the same way Christians question the faith of other religions, we have no right to do this.
the only certainty is that we will all have the same opportunity for liberation.
Christianity is a religion consoling, not punitive.

ah i see what you ment by infinity different infinities, though in a sense, if you calculate it out, they are all just aspects of the original infinity.

similar to how you can say this infinate family is going to all prime rooms, you can say this family is going to 3^2 then 3^2^2 then 3^2^2^2 then 3^2^2^2^2 ect

This post was edited by Ylem122 on May 3 2013 10:33am