I think that would also be the case outside a black hole. The way I see it, mass/energy and spacetime curvature are just two different ways of describing the same 'thing'. Helps with a black hole though, since you have the problem that if mass is inside the event horizon, how can it affect...
The mass required for BH formation isn't the clear cut, also depends on star composition and the type of supernova. It's possible that very large mass stars leave neutron stars rather than blacks holes, or even no remnant at all - depends how much mass is lost in the supernova. I have a diagram...
The visible clouds are ammonia ice, probably water ice clouds lower down. Pretty sure that's where most of the ice is. Density with Jupiter is extreme, there may even be electron degenerate matter at the core, similar to that in White Dwarfs. Can't imagine much 'ice' there, mainly iron I would...
Not sure, would the numbers be entangled? Maybe some quantum computing algorithm...
Ok, I did a physics degree a few years ago, having a background in maths, and I have to say that some of the maths that physicists do did strike me as, well, heresy, almost.
Well, that's the convention I use, as I said, less confusing, but at the end of the day it might well come down to whether you are doing maths or physics, or whatever problem you are solving - often you are only interested in positive values, or real numbers, though not always.
sqrt(-1) is one root (a function), (-1)^1/2 = +/- sqrt(-1) is both roots (not a function) ...as far as I know, I could be wrong. Computers treat them the same, but they are dumb. My thinking is it's direct from x2 = -1 --> x(2 x 1/2) = (-1)(1 x 1/2) ---> x = (-1)1/2. Not specifying a specific...
You sure about that, the number? or numbers? It's used both ways, although I'm pretty sure it's defined as principle root, which is why you usually see a +/- before it.
So that makes you half wrong. (-1)^1/2 is less ambiguous.
Learning as you go - bear in mind you will be judged on your work. Sure, you can learn some stuff as you go, but it's going to take time, and no client is going to want to pay for that, unless it is something really rare that hardly anyone knows, which also happens. In fact a lot clients use...
Yes, when I started I was living in Bulgaria, where $10/hr is pretty good. SE Asia is the worst, I have seen them charging $3/hr. They do have a bad rep though, so that might be in your favour. Sometimes you can get more, I got $80/hr one time for a client that wanted the job done asap, but...
There are several freelancer sites - basically you sign up to these, clients post jobs that you bid for, the site take a percentage of your fee. In some cases you build up a long term relationship with a client and move off the site, once you trust each other. That's basically how I operated for...
There are several freelance sites you can sign up to, so why not give it a try? But, don't expect much. There is a lot of competition, much from people who are happy to charge less than $5 per hour, so unless you can offer something they can't, you are not going to earn much.