The smallest positive integer is

(a) 0

(b) 100

(c) 1

(d) 9

The smallest positive integer is (c) 1. Let's break down why this is the case and clarify the concept of positive integers.

Understanding Positive Integers

Positive integers are the set of whole numbers greater than zero. This means they start from 1 and continue infinitely: 1, 2, 3, 4, and so on. It's important to note that zero is not considered a positive integer; it is classified as a non-negative integer.

Examining the Options

Now, let’s look at the options provided:

• 0: This is not a positive integer; it is simply zero.
• 100: While this is a positive integer, it is not the smallest one.
• 1: This is indeed the smallest positive integer.
• 9: Like 100, this is a positive integer but not the smallest.

Why 1 is the Smallest

To further illustrate why 1 is the smallest positive integer, consider the definition of "smallest." In a numerical sense, when we compare numbers, 1 is less than any other positive integer. For example, if you have a number line, 1 is the first point you encounter when moving right from zero.

Real-World Analogy

Think of counting objects. If you have one apple, you can say you have a positive quantity of apples. If you had zero apples, you wouldn't have any apples to count. Thus, the act of counting starts at 1, reinforcing that it is the smallest positive integer.

Conclusion

In summary, the smallest positive integer is 1. It serves as the foundation for counting and is the first number in the set of positive integers. Understanding this concept is crucial for various mathematical applications, from basic arithmetic to more complex number theory.