Quote:
Originally Posted by 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. |
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.