Raymond B. answered • 08/17/21
Math, microeconomics or criminal justice
an integer is a member of the set {...-3, -2, -1, 0, 1, 2, 3, ...}
a rational number is any number that can be written as a fraction, a/b, where both numerator and denominator are integers.
all integers are rational numbers, but all rational numbers are not integers.
5/5, 6/3, -3006/1002 are all rational numbers and also integers, as 5/5=1, 6/3=2, -3006/1002 =-3
integers are a subset of rational numbers
but rational numbers include far more than just integers.
natural or counting numbers are the set {1,2,3,4, ...}
they are a subset of whole numbers, the set {0,1,2,3,4,...}
they are both subsets of the set of integers,
they all are subsets of rational numbers
which is a subset of real numbers. All rational numbers are real numbers, but not all real numbers are rational numbers
If you drew a Venn diagram, with the rectangle as the universe as the set of all real numbers, and a circle inside to represent rational numbers, the integers would be another circle inside the circle of all rational numbers. the two circle would not overlap. The integer circle would be completely inside the circle of rational numbers.
