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A discrete mathematical propagating model of the electrocardiogram is derived and used to describe and analyze a number of T-wave concepts: ventricular gradient, primary, secondary, and intrinsic T-waves. Several previously accepted, but inadequately justified ideas are precisely defined and rigorously developed. These include ventricular gradient, conditions for zero ventricular gradient, and the gradient's independence of activation sequence. Several new results are derived as well. Specifically, more general conditions for zero ventricular gradient in all leads are defined, the concepts of primary and intrinsic, as well as secondary T-waves are mathematically defined, it is shown that it is impossible to obtain the primary T-wave from the recorded and secondary T-waves by linear operations as has been suggested, the secondary T-wave is shown to be not uniquely definable, and computer-generated simulations illustrating many of the results are presented.