premjan

is the difference between power sets used in the diagonal argument?

This is why mathematics is historically one of the liberal arts.

your "proof" that Cantor is wrong depends on his use of 2^aleph0 for the magnitude of R. This notation is not compulsory, and in hindsight perhaps ought to be discarded. What Cantor ought to have said was "power set" instead of 2^aleph0. Unfortunately Cantor is not here to explain himself.

You can prove that A is the limit of B only if you can show that s'=0_AND_s'=1 -> 1 I don't understand this line at all. Isn't the AND a contradiction?

simply does not hold because of asymmetry, but I hardly consider that a law in the same vein as e=mc^2.

as for the incorrectness of ZF proofs, you have to show this by an actual counterexample, just saying that the system has a flaw is not likely to be good enough.

the problem is that proofs are generally designed for people (mathematicians) to follow, not for computers. Your approach might reduce the number of steps for a proof, especially a mechanical proof, which might make it useful in computer theorem provers.

b = (G^2 * h^2) ^(1/7) a = G c = (Gh)^(3/7) d = (h/M) * (G*h)^(5/7) I didn't plug it back into everything to check. It is actually a fairly simple system to solve.

I think your approach is more amenable to a computer algorithm than to proofs (which is what mathematicians traditionally do more of). Maybe you are posting in the wrong section?

I think this last definition obviates the need for a proof (more of proof by examination than anything).

I think this last definition obviates the need for a proof (more of proof by examination than anything).

you should use the following definition of sin, then it is very easy to reconcile. draw a unit circle centered at (0,0). let the angle theta be the angle that a radius of this circle makes with the +x axis. Let sin theta be the ratio y/r where (x,y) is the point at which the given radius intersects the circle (there is only one such point). Then use the reflection argument which I gave you earlier.

you should use the following definition of sin, then it is very easy to reconcile. draw a unit circle centered at (0,0). let the angle theta be the angle that a radius of this circle makes with the +x axis. Let sin theta be the ratio y/r where (x,y) is the point at which the given radius intersects the circle (there is only one such point). Then use the reflection argument which I gave you earlier.

the question is how to systematically eliminate duplicates (one + or - is as good as another), given that we cannot flip the circle over.

the question is how to systematically eliminate duplicates (one + or - is as good as another), given that we cannot flip the circle over.

wouldn't a non-inverted retina raise the problem of not having a uniformly curved (spherical ideally) retina? it would be like projecting onto a wavy screen unless the retinal cells (long structures as I gather they are) were substantially rigid.

wouldn't a non-inverted retina raise the problem of not having a uniformly curved (spherical ideally) retina? it would be like projecting onto a wavy screen unless the retinal cells (long structures as I gather they are) were substantially rigid.

what is the definition of sin(theta) that you use? Assuming that it is opposite/hypotenuse, how would you extend this to the case where theta > 90? for that matter, how do you reconcile the fact that at 90deg, there is effectively no right triangle at all?

what is the definition of sin(theta) that you use? Assuming that it is opposite/hypotenuse, how would you extend this to the case where theta > 90? for that matter, how do you reconcile the fact that at 90deg, there is effectively no right triangle at all?

you have two different unknowns: y and f, so you don't appear to have enough information to produce a solution with only one equation.

you have two different unknowns: y and f, so you don't appear to have enough information to produce a solution with only one equation.

just set r=1, and draw the diagram. it is rather obvious and I am uncertain what steps a formal geometric proof could require. Basically, the angle 180-A is obtained by reflection of the angle A around the y-axis, so pretty much by that definition, the y-coordinate remains the same, and r is not going to change since it is a circle.

just set r=1, and draw the diagram. it is rather obvious and I am uncertain what steps a formal geometric proof could require. Basically, the angle 180-A is obtained by reflection of the angle A around the y-axis, so pretty much by that definition, the y-coordinate remains the same, and r is not going to change since it is a circle.

I'm thinking that the unit circle was probably used to define all the trig ratios. If you draw a unit circle and then look at the radius line that makes an angle starting from 0deg to 360 deg turning ccw, you could easily prove the various trig identities.

I'm thinking that the unit circle was probably used to define all the trig ratios. If you draw a unit circle and then look at the radius line that makes an angle starting from 0deg to 360 deg turning ccw, you could easily prove the various trig identities.