Section 1.7
... 3.) Solution Set – set of all solutions of the sentence that belong to a given domain of the variable and make the sentence true. Note: Unless otherwise stated, our domain will always be the set of real #’s ( ) . 4.) Equivalent Equations – equations that have the same solution set over a given domai ...
... 3.) Solution Set – set of all solutions of the sentence that belong to a given domain of the variable and make the sentence true. Note: Unless otherwise stated, our domain will always be the set of real #’s ( ) . 4.) Equivalent Equations – equations that have the same solution set over a given domai ...
BKL singularity
A BKL (Belinsky–Khalatnikov–Lifshitz) singularity is a model of the dynamic evolution of the Universe near the initial singularity, described by an anisotropic, homogeneous, chaotic solution to Einstein's field equations of gravitation. According to this model, the Universe is oscillating (expanding and contracting) around a singular point (singularity) in which time and space become equal to zero. This singularity is physically real in the sense that it is a necessary property of the solution, and will appear also in the exact solution of those equations. The singularity is not artificially created by the assumptions and simplifications made by the other well-known special solutions such as the Friedmann–Lemaître–Robertson–Walker, quasi-isotropic, and Kasner solutions.The Mixmaster universe is a solution to general relativity that exhibits properties similar to those discussed by BKL.