Which statement is false?
A: Every integer is a real number.
B: the number zero is a rational number.
C: every irrational number is a real number.
D: every real number is a rational number****
To determine which statement is false, let's examine each statement individually:
Statement A: Every integer is a real number.
This statement is true. Every integer is indeed a real number because integers are a subset of the real numbers.
Statement B: The number zero is a rational number.
This statement is true. Zero is indeed a rational number because it can be expressed as the ratio of two integers (0/1 or any other fraction with 0 as the numerator).
Statement C: Every irrational number is a real number.
This statement is true. Every irrational number is a real number because irrational numbers cannot be expressed as a fraction and still exist on the number line.
Statement D: Every real number is a rational number.
This statement is false. Not every real number is a rational number. A rational number can be expressed as a fraction where both the numerator and denominator are integers. Irrational numbers, such as the square root of 2 or pi, cannot be expressed as a fraction and are therefore not rational.
Therefore, the false statement is D: Every real number is a rational number.