Which family of numbers begins with the numbers 0, 1, 2, 3, ...?
A. Natural numbers
B. Whole numbers
C. Real numbers
D. Rational numbers
E. Integers
Answer (2)
The family of numbers starting with 0, 1, 2, 3, ... is the set of whole numbers, which includes all natural numbers plus zero. Other families like natural numbers start from 1 and do not include 0. Therefore, the chosen answer is Whole numbers.
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Define the number families: natural, whole, integers, rational, and real numbers.
Identify that whole numbers include 0, 1, 2, 3, ...
Exclude other options based on their definitions.
Conclude that the correct answer is \boxed{Whole numbers}.
Explanation
Understanding the Question We need to identify the family of numbers that starts with 0, 1, 2, 3, ... To do this, we will consider the definitions of the given number families.
Defining Number Families Let's define each number family:
Natural numbers: These are positive integers starting from 1 (i.e., 1, 2, 3, ...).
Whole numbers: These include all natural numbers and zero (i.e., 0, 1, 2, 3, ...).
Integers: These include all whole numbers and their negatives (i.e., ..., -2, -1, 0, 1, 2, 3, ...).
Rational numbers: These are numbers that can be expressed as a fraction q p , where p and q are integers and q = 0 . Examples include 2 1 , − 4 3 , and 5 (since 5 = 1 5 ).
Real numbers: These include all rational and irrational numbers. Irrational numbers are numbers that cannot be expressed as a fraction of two integers (e.g., 2 , π ).
Identifying the Correct Number Family Based on the definitions, the family of numbers that begins with 0, 1, 2, 3, ... is the set of whole numbers.
Final Answer Therefore, the correct answer is Whole numbers .
Examples
Understanding number families is fundamental in many areas of mathematics and everyday life. For instance, when counting objects, we use natural numbers. When representing quantities that can be zero, like the number of apples in a basket, we use whole numbers. Integers are useful for representing temperatures above and below zero, while rational numbers are used in measurements and proportions, such as dividing a pizza into slices. Real numbers encompass all these and are crucial in advanced mathematics and physics.
