lösningmängd

A lösningmängd, which translates to "solution set" in English, is a fundamental concept in mathematics, particularly in the study of equations and inequalities. It represents the collection of all possible values for the variable(s) that make a given equation or inequality true.

For an equation, the lösningmängd contains all the numbers that, when substituted for the variable, result in a true statement. For example, the lösningmängd for the equation x + 2 = 5 is {3}, because only 3 satisfies the equation. If an equation has no solutions, its lösningmängd is the empty set, denoted by {} or Ø. An equation with infinitely many solutions, such as x = x, has a lösningmängd that includes all real numbers.

Similarly, for an inequality, the lösningmängd comprises all values of the variable that make the inequality true. For instance, the lösningmängd for x > 2 is all numbers greater than 2, which can be represented in interval notation as (2, ∞). The nature of the inequality (strict or inclusive) determines whether the endpoints are included in the lösningmängd.

Understanding the lösningmängd is crucial for solving mathematical problems, as it provides a clear definition of what constitutes a valid answer. It is a core concept in algebra, calculus, and many other branches of mathematics.