Lösningsmängd

Lösningsmängd is a Swedish term that translates to "solution set" in English. It refers to the collection of all possible values of a variable that satisfy a given equation or inequality. In mathematics, when we solve an equation or inequality, the lösningsmängd is the set of numbers that make the statement true.

For example, if we consider the equation $2x = 6$, the lösningsmängd is the set containing only the value 3, because $2 \times 3 = 6$. If the equation had no solution, the lösningsmängd would be an empty set. For inequalities, the lösningsmängd can be an infinite set of numbers. For instance, the inequality $x > 5$ has a lösningsmängd of all real numbers greater than 5.

The concept of lösningsmängd is fundamental in algebra and various branches of mathematics. It helps in understanding the scope of possible outcomes for mathematical problems and is crucial for analyzing the behavior of functions and systems of equations. The representation of the lösningsmängd can vary, often using set notation or interval notation. Understanding what constitutes the lösningsmängd is key to correctly interpreting the results of mathematical manipulations.