Integer

The integers are the set {…, −3, −2, −1, 0, 1, 2, 3, …} — every positive whole number, every negative whole number, and zero. The defining property is the absence of any fractional or decimal part. So 14, −200, and 0 are integers, while 1/2, −3.7, and √2 are not.

Two common questions have quick answers. Are fractions integers? Not unless they simplify to a whole value: 8/4 equals the integer 2, but 3/4 is not an integer. Can integers be decimals? A number written with a decimal point is an integer only if the decimal part is zero — 5.0 is the integer 5, but 5.1 is not. Also remember that zero is an integer (neither positive nor negative), and every negative whole number counts too.

Integers have properties that standardized tests exploit constantly. They are closed under addition, subtraction, and multiplication — combining integers those ways always produces another integer — but not under division (7 ÷ 2 = 3.5). Every integer is either even or odd, and even/odd rules (odd + odd = even, odd × odd = odd) power many number properties questions. Integers also form the backbone of concepts like factors, multiples, and remainders.

Number properties are heavily tested on college entrance and teacher certification exams. The CLT and SAT ask questions that hinge on recognizing which values are integers, and the Praxis Core math test covers integers, decimals, and fractions as a foundational topic.