Zero is an integer that is neither positive nor negative. True False
The correct answer and explanation is:
True.
Zero is indeed an integer that is neither positive nor negative. It serves as the neutral element in the set of integers. In mathematics, the integers are a set that includes all positive whole numbers, all negative whole numbers, and zero itself. Therefore, integers are represented as {…, -3, -2, -1, 0, 1, 2, 3, …}.
Zero is unique in the sense that it is the only integer that is neither positive nor negative. This characteristic is important for various reasons in both basic arithmetic and advanced mathematical operations. For instance, when dealing with arithmetic operations like addition, subtraction, or multiplication, zero behaves in a distinctive way. For addition, adding zero to any number does not change the value of the number (i.e., x+0=xx + 0 = x). For multiplication, any number multiplied by zero equals zero (i.e., x×0=0x \times 0 = 0).
Zero also has an essential role in defining concepts like the additive identity, which states that zero is the element that leaves other numbers unchanged when added. Moreover, in many number systems, zero serves as the starting point, such as in counting, where you start from zero rather than one.
The idea that zero is neither positive nor negative reflects its neutral position in the number line, and this quality is significant in various fields of study, including calculus, algebra, and number theory. It is a fundamental concept in understanding the structure of numbers and their properties.