mathematic

Standard formula would be n(n+1)/2 -k(k-1)/2.

The paper is basically flawed. All it does is count all reals with finite decimal expansions - a countable list, but certainly not all reals. ! Moderator Note Merged with the open thread on this subject

The most important math background would be differential geometry.

Cosmic rays may not be a serious problem. The Apollo program did not concern itself with them.

The world is a physcial entity. The things you mention are possible mathematical models.

Uncountable numbers are best described by being, like the real numbers. There are proofs that they are not countable.

It sounds awfully offbeat as far as quantum theory is concerned.

Has there been any progress in recent years to unify relativity with quantum theory? I have the impression that both string theory an loop quantum gravity have not made any progress recently,

Go to a math librayr or a college library and look at the math journals. Usually they describe how to submit something for publication.

Don't confuse infinity, which is a math concept, with what is physically possible.

Vector sum gives magnitude and direction for acceleration.

Doubtful. If it is for real, submit it to math journal.

Look in control panel for "sound". Check settings to handle your devices.

Supercritical water is at a much lower density than liquid water. It is easily compressible.

a=2mn, b=m^2-n^2,c=m^2+n^2