It seems quite obvious now that Barry does not want to learn anything and is trying to push his own personal theories. Is there a way to request thread lock? :uhh:
Nope. Energy is constant for a given photon. You just wrote down the equation. Both h and f are constants (h is universal constant, f is constant for a given photon) so E must also be constant. Keep in mind that frequency tells you how many cycles are there per second and so it does not change...
It's not just a problem of applicability of equations. Have you tried solving Schrodinger equation for that problem? It's ridiculous compared to the simple classical solution. :yuck:
Thanks, now I understand where the 7% comes from. But I still don't get why negative curvature means finite universe. Can't infinite universe have negative curvature as well?
The usual proof of this theorem seems to assume that the topology of the metric space is the one generated by the metric. But if I use another topology, for example the trivial, the space need not be Hausdorff but the metric stays the same. Am I missing something or is the statement of the...
I don't think it's meaningless. In introductory classes (where vectors aren't even defined properly) rows and columns are often just different notations for components of vectors.
If you're talking about simple real vectors (e.g. arrows in euclidian space) than the transposed vector is the same as the original. It's merely a matter of notation,whether you write the components in row or column.
In general case there is a distinction between row vectors and column vectors...
What I find most confusing about topology is that there seem to be many similar (or related) definitions and concepts and not enough examples for them. It helps a lot when I know an example that comes with definition because even when I forget parts of the definition I can always fill the blanks...
This is not true. You cannot do so in real numbers because ∞ is not defined on reals, but there exists the extended real number line, which defines +∞ and -∞. You CAN do some arithmetic operations on infinity in such case. It is commonly used when doing calculus, when computing limits for...