Mathematical conundrums in the standard theory of special relativity

Although written in 1905, Einstein's Special Theory of Relativity, published in his Zur Elektrodynamik bewegter Körper (On the Electrodynamics of Moving Bodies), is still considered the standard theoretical approach in relativistic physics to measure and explain the relationship between space (and/or length in the direction of motion) and time within different frames of reference. We assess in the present work some of the mathematical implications of this relativistic physics and show that using the premise "0 = 0" to build a theory of special relativity would lead to incorrect mathematical conclusions such as A = -A or 1 = -1.