300 year equation

[temur]

After over 300 years, the issue of whether 0.999... = 1 remains unresolved

And whether GR is self-consistent, and whether all matter is made of photons...

 

[Absane]

After over 300 years, the issue of whether 0.999... = 1 remains unresolved

You should be PERMANENTLY BANNED after bring this "problem" into the light.

Heh.. jk.

And whether GR is self-consistent, and whether all matter is made of photons...

The existence of UFOs shows that both cases are two. The one that crashed in Roswell posses all those, and more.

 

[Cyperium]

After over 300 years, the issue of whether 0.999... = 1 remains unresolved

I suppose you are joking?

Otherwise look here...

 

[przyk]

I suppose you are joking?

Of course. "0.999... = 1" incites fear and loathing among the members who've been around here a while and know what an infinite series is.

 

[Absane]

Of course. "0.999... = 1" incites fear and loathing among the members who've been around here a while and know what an infinite series is.

Oh man, yes.

They argue with their imaginations and faulty intuitions while I crack open my analysis book (Principles of Mathematical Analysis by Rudin) and preach from the quire.

I had some good times in the past.. but I'm too old (25) to argue anymore. My back is bad and my social security check is running late this month. My grandchildren don't visit anymore...

 

[science man]

Well if you tried to solve the exact equations for many physical systems then yes it would take well over 300 years for any individual or computer to solve. I mean if you wanted to solve the exact quantum mechanical properties of 1g of matter that would mean solving a differential equation (Schrodinger equation) with around 10^23 particles. And each of these particles has a pairwise interaction with every other particle.

Even if you could get a solution it would take an equally long time to interpret it. Considering that at the moment as far as I know for the best computational methods, the computing time is proportional to the number of particles and it has currently been done for a few hundred atoms thenn you can see 10^23 particles would take a long time.

so what is the actual equation?

 

[science man]

The joys of google:

$$ B_m=\sum_{k=1}^{m+1}\sum_{v=1}^{k+1}(-1)^{v+1}\binom{k-1}{v-1}\frac{v^m}k $$

This is one of many. The most obvious formula comes from a "multiply-differentiate-limit" approach to the generating function.

you found a list of these equations? where? because I tried to google for them but no luck.

 

[Absane]

There are some on Wiki...

 

[science man]

but what would u type into weikipedia

 

[SFinn]

but what would u type into weikipedia

0.999

(if you were inquiring as to which Wikipedia article)

 

[BobG]

so what is the actual equation?

Well you'd solve the time independent Schrodinger_equation, H|psi> = E|psi> where a realistic H for a solid is given by

The first two terms take into account the Kinetic energy of all the particles and the rest take into account the ion-electron, electron-electron and ion-ion attractions. The sums are between every possible pair of particles which means for a large number of particles like in a realistic solid it will take a pretty long time to solve even if you stick in a computer looking for a numerical solution.

 

[krazedkat]

inf+1=x


try it, I dare you