15_cardinality
... inverse Proof (⇒): If it is bijective, it has a left inverse (since injective) and a right inverse (since surjective), which must be one and the same by the previous factoid Proof (⇐): If it has a two-sided inverse, it is both injective (since there is a left inverse) and surjective (since there is ...
... inverse Proof (⇒): If it is bijective, it has a left inverse (since injective) and a right inverse (since surjective), which must be one and the same by the previous factoid Proof (⇐): If it has a two-sided inverse, it is both injective (since there is a left inverse) and surjective (since there is ...
Revised Version 070511
... However, this claim is exactly what we are trying to show. The model for direct proportion, y = kx , suggests a family of lines through the origin. For y and non-zero x as the coordinates of points on a line given by y y=kx, the ratio equals k, which is constant. If this ratio held for the x ...
... However, this claim is exactly what we are trying to show. The model for direct proportion, y = kx , suggests a family of lines through the origin. For y and non-zero x as the coordinates of points on a line given by y y=kx, the ratio equals k, which is constant. If this ratio held for the x ...
Mathematics of radio engineering
The mathematics of radio engineering is the mathematical description by complex analysis of the electromagnetic theory applied to radio. Waves have been studied since ancient times and many different techniques have developed of which the most useful idea is the superposition principle which apply to radio waves. The Huygen's principle, which says that each wavefront creates an infinite number of new wavefronts that can be added, is the base for this analysis.