ABSTRACT
Open and closed intervals generalize to open and closed sets, which respectively exclude and include the boundary elements. A member of a set is either less than or equal to the lower bound. Similarly, a set member is either greater than or equal to the upper bound. Any non-autonomous differential equation can be transformed into a set of autonomous differential equations by introducing additional state variables. According to the Bolzano—Weierstrass Theorem, there is at least one point of accumulation (or limit point) in a bounded set having an infinite number of elements. Alternatively, each bounded sequence in the set has a subsequence that converges to a point in the set. A linear or vector space is a set of elements known as vectors for which the following two operations: addition of vectors and multiplication of a vector by real numbers are defined. The set of real numbers for which the usual addition and multiplication are defined.
