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Re: Game theory: Factorio takes place on Earth
Posted: Wed Dec 27, 2017 3:51 am
by Jap2.0
Zavian wrote:Jap2.0 wrote:Koub wrote:I'd say that for a sphere, you need a center, and a radius. Thus, there is no such thing as an infinite sphere.
The radius is infinity, the center is, well, wherever you want it - although technically infinity is a concept, not a number (although that's how it's often used).
Well the center has to be infinitely far away from the surface of the sphere, so it's not as unrestricted as "wherever you want it".
Is infinity minus 1 still infinity?
Re: Game theory: Factorio takes place on Earth
Posted: Wed Dec 27, 2017 4:42 am
by 5thHorseman
Jap2.0 wrote:Zavian wrote:Jap2.0 wrote:Koub wrote:I'd say that for a sphere, you need a center, and a radius. Thus, there is no such thing as an infinite sphere.
The radius is infinity, the center is, well, wherever you want it - although technically infinity is a concept, not a number (although that's how it's often used).
Well the center has to be infinitely far away from the surface of the sphere, so it's not as unrestricted as "wherever you want it".
Is infinity minus 1 still infinity?
Yes.
But don't ask about infinity minus infinity or infinity divided by infinity. Those get a bit more complicated.
Re: Game theory: Factorio takes place on Earth
Posted: Wed Dec 27, 2017 5:42 pm
by Jap2.0
+/
5thHorseman wrote:Jap2.0 wrote:Zavian wrote:Jap2.0 wrote:Koub wrote:I'd say that for a sphere, you need a center, and a radius. Thus, there is no such thing as an infinite sphere.
The radius is infinity, the center is, well, wherever you want it - although technically infinity is a concept, not a number (although that's how it's often used).
Well the center has to be infinitely far away from the surface of the sphere, so it's not as unrestricted as "wherever you want it".
Is infinity minus 1 still infinity?
Yes.
But don't ask about infinity minus infinity or infinity divided by infinity. Those get a bit more complicated.
So then the center can be anywhere, because the location is infinity minus one away from one edge and infinity plus one away from the other.
Re: Game theory: Factorio takes place on Earth
Posted: Thu Apr 05, 2018 1:41 am
by thereaverofdarkness
Jap2.0 wrote:So then the center can be anywhere, because the location is infinity minus one away from one edge and infinity plus one away from the other.
No, it can only be in one place; that place is impossible to define in real numbers. It cannot, for instance, be three meters below the surface.
Re: Game theory: Factorio takes place on Earth
Posted: Thu Apr 05, 2018 10:47 am
by Frightning
olafthecat wrote:Surely the planet could be an infinite sphere?
infinite in what way? Even the unit sphere has (uncountably) infinitely many points on its surface.
Re: Game theory: Factorio takes place on Earth
Posted: Thu Apr 05, 2018 12:41 pm
by 5thHorseman
Frightning wrote:olafthecat wrote:Surely the planet could be an infinite sphere?
infinite in what way? Even the unit sphere has (uncountably) infinitely many points on its surface.
I would assume infinite in the only way that makes any sense in this discussion: It's impossible to circumnavigate at any (non-infinite) speed.