real or imaginary reciprocity

[AntonioLao]

Both rationals and irrationals possess reciprocals. The definition is simply the product of a real number r by its reciprocal 1/r such that the answer is the identity of multiplication. However, the graph of a reciprocal function f(x)=1/x is equivalent to the graph of an inverse variation such that if the function is y then the product of xy=k is a constant k. On the other hand, the general equation of a conic is a second degree equation given by Ax+Bxy+Cy+Dx+Ey+F=0, where A, B, C, D, E, F are real numbers and A, B, C are not all zero. If A=C=F=0, B=D=1, and E=-1 then the equation is reduced to xy=y-x. Solving for y gives the rational function y=x/(1-x). However, if A=C=D=E=0 then Bxy+F=0 is equivalent to xy=k where k=F/B.

The analysis of both of these functions: xy=k and y=x/(1-x) by graphical calculations suggested strong implication of real reciprocity between zero and infinity versus unity and infinity. Nonetheless only the function xy=y-x could give the singular isolated solution where x and y are both zero.

[mkirkpatrick]

Both rationals and irrationals possess reciprocals. The definition is simply the product of a real number r by its reciprocal 1/r such that the answer is the identity of multiplication. However, the graph of a reciprocal function f(x)=1/x is equivalent to the graph of an inverse variation such that if the function is y then the product of xy=k is a constant k. On the other hand, the general equation of a conic is a second degree equation given by Ax+Bxy+Cy+Dx+Ey+F=0, where A, B, C, D, E, F are real numbers and A, B, C are not all zero. If A=C=F=0, B=D=1, and E=-1 then the equation is reduced to xy=y-x. Solving for y gives the rational function y=x/(1-x). However, if A=C=D=E=0 then Bxy+F=0 is equivalent to xy=k where k=F/B.

The analysis of both of these functions: xy=k and y=x/(1-x) by graphical calculations suggested strong implication of real reciprocity between zero and infinity versus unity and infinity. Nonetheless only the function xy=y-x could give the singular isolated solution where x and y are both zero.

We need a "real" point of entry here I feel.imaginary will not cut the mustard!

To gain a foothold on mobius we must be "real".


regards michael.

[AntonioLao]

To gain a foothold on mobius

But its physical dimension is less than three dimensional?

[mkirkpatrick]

But its physical dimension is less than three dimensional?

Don't fret there is a way,I can feel it in my water!



regards michael.

[AntonioLao]

Don't fret there is a way

The only way I'm suggesting is to stop the flow of time. Once time is stopped then infinite consciousness is realized.

[mkirkpatrick]

The only way I'm suggesting is to stop the flow of time. Once time is stopped then infinite consciousness is realized.

Exactly and with infinite consciousness in the driving seat,all becomes realizable.


regards michael.