List all the numbers given set that a natural numbers be whole numbers c integers d rational numbers e irrational numbers f real numbers
Each of those sets is infinite. You cannot list all the numbers in any of them.
Choose what groups the number -11 belongs. Select ALL that apply.
a. Natural Numbers
b. Real Numbers
C. Integers
d. Whole Numbers
e. Rational Numbers
f. Irrational Numbers
To list the numbers in each set, we need to understand what each set represents. Here is an explanation of each set and how to determine the numbers within them:
a) Natural numbers: These are the counting numbers, starting from 1 and going infinitely. The set of natural numbers can be denoted as N = {1, 2, 3, 4, ...}.
b) Whole numbers: Whole numbers include all the natural numbers (counting numbers), as well as the number 0. The set of whole numbers can be denoted as W = {0, 1, 2, 3, 4, ...}.
c) Integers: Integers include all the whole numbers (including 0), as well as their negatives. The set of integers can be denoted as Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}.
d) Rational numbers: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. This means that a rational number can be written in the form of a/b, where a and b are integers and b is not equal to 0. Rational numbers include integers and fractions. For example, 1/2, -3/4, and 5 are all rational numbers. The set of rational numbers can be denoted as Q.
e) Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. These numbers are non-repeating and non-terminating decimals. Examples of irrational numbers include √2, π (pi), and e (Euler's number). The set of irrational numbers can be denoted as I.
f) Real numbers: Real numbers include both rational numbers and irrational numbers. In other words, real numbers include all numbers that can be represented on a number line. So the set of real numbers is R = Q ∪ I.
To summarize, here are the numbers in each set:
a) Natural numbers: N = {1, 2, 3, 4, ...}
b) Whole numbers: W = {0, 1, 2, 3, 4, ...}
c) Integers: Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}
d) Rational numbers: Q (includes integers and fractions)
e) Irrational numbers: I
f) Real numbers: R (includes both rational and irrational numbers)