Gleichsetzens

Gleichsetzens is a term used in German-language mathematics to describe the process of setting two expressions equal to each other, typically to determine unknown quantities or to verify algebraic identities. It is commonly encountered in solving equations and in proving that two expressions represent the same quantity under given conditions.

In practice, Gleichsetzens encompasses techniques centered on converting a problem into an equality and manipulating it with algebraic rules. This includes isolating a variable, rearranging terms, and substituting an expression that is known to be equivalent. It can be applied to linear and nonlinear equations, systems of equations, and problems in analytic geometry where parameters are determined by equality constraints.

Examples: 1) Solve x+3=7 by Gleichsetzen of the two sides and subtracting 3 from both sides to obtain x=4. 2) For a system a+b=5 and b=2a, Gleichsetzen means replacing b with 2a in the first equation, yielding a+2a=5 and hence a=5/3.

The concept is closely related to substitution and elimination techniques used in algebra. It should not be confused with Gleichsetzung in logic, which refers to declaring two terms equal in a formal sense. In educational contexts, Gleichsetzens is a practical description of the stepwise process of enforcing equality between expressions to reach a solution.