Real numbers - practice problems

Real numbers include all rational numbers (integers, fractions) and irrational numbers (non-repeating, non-terminating decimals), forming a complete ordered set that can be represented on the number line. Every point on the number line corresponds to exactly one real number. Real numbers support all standard arithmetic operations and ordering relationships. Key subsets include natural numbers, whole numbers, integers, rational numbers, and irrational numbers like √2 and π. Properties of real numbers include closure, commutativity, associativity, identity elements, and inverses for addition and multiplication. Understanding real numbers is fundamental to algebra, calculus, and most mathematical applications in science and engineering.

Directions: Provide a careful solution to each problem, showing all steps in your work.

Number of problems found: 162


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