mathematic

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.

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

14 minutes ago, uncool said:

There are countably many triplets of integers (a, b, c) such that a^2 + b^2 = 2c^2. There's even a method to find them.

Do you know how to find a triplet (a, b, c) such that a^2 + b^2 = c^2?

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

I can't tell what the angles associated with the numbers are.  Mark beginning and end of each angle.

Habitable planet zone means it is possible, not certain that a planet could support life.

Draw a diagram.

23 hours ago, nevim said:

It’s usual to get a higher reading of both at the wrist.

My readings:  Systolic much higher at arm, Diastolic approximately the same for both.

I have two instruments for measuring my blood pressure, arm and wrist.  The diastolic readings (lower) tend to agree.  However the systolic (higher) readings tend to be far apart.  The arm reading runs about 30 points higher.  Is this a meaningful difference or a sign of instrument error?

dx etc. are symbols used for derivatives and integrals.  They are not supposed to have numeric values.

22 hours ago, uncool said:

This isn't exactly true; the actual definition involves lots of "there exists" and "for all"s. If the function is nice enough, then yes, this "pseudo-proof" tells you that the second derivative must be equal to the expression given; however, the second derivative does not necessarily exist.

I have assumed all these niceties are in place, so I answered the question as posed.

You can use it. f'(x)=(f(x+dx)-f(x))/dx.  f'''(x)=(f'{x+dx)-f'(x))/dx is exactly the expression  you gave.

It loos like an ordinary (not partial) diff. eq. in r.  Which symbols represent functions of r?

Light bulb is ordinary (old fashioned) incandescent.  House is private home - no one else to handle circuit breaker.   Filament breaking and reconnect seems only possible, even if improbable, explanation.

Your question needs elaboration.

Try Amazon.

I presume there is something which prevents the weight from sinking.  Weight of water in tube equals weight of water in basin + 10 kg.  If wight sinks to the bottom, it can be ignored and the weight in the basis = weight in tube.

Energy is used to describe photons, etc. which have no rest mast.  Pure is a popular term which means there are no particles with mass, such as electrons, quarks, etc.  The fundamental question that is under discussion here is why is there matter now?

Forward time travel needs only special relativity.  Go from here to some place, say ten light years away, at near the speed of light, so the journey for you is a matter of days.  Now turn around and go back to earth at the same speed.  For you the time elapsed is a matter of some number of days, but when you get back to earth it will be twenty years later.