Question

The smallest positive integer is_____

Answer 1

Hint: In this question, we need to find the smallest positive integer. For this, we will first state the definition and set of integers. After that, we will omit all the negative or zero integers to get a set of positive integers. From this set, we will find our required smallest positive integer.

Complete step by step answer:
Here, we need to find the smallest positive integer. For this, let us first understand what integers are.
Integers are the numbers that can be positive, negative, or zero but cannot be a fraction. It basically consists of the zero, set of whole numbers and their additive inverses. Examples of integers are: -99, 87, 42, 0, -69, -5 etc.
In the set representation, a set of integers is denoted by Z given as,
\[Z=\left\{ \ldots \ldots -3,-2,-1,0,1,2,3,\ldots \ldots \right\}\].
In this question, we are dealing only with positive integers, so we should delete negative integers from the set. Since zero is neither positive nor negative, we will not consider it in the set of positive integers. Hence, our set of positive integers denoted by $ {{Z}^{+}} $ will look like this,
 $ {{Z}^{+}}=\left\{ 1,2,3,4,\ldots \ldots \right\} $ .
As we can see, 1 is the smallest number in this set. Therefore, the smallest positive integer is 1.

Note:
 Students can make mistakes of considering 0 in the set of positive integers which makes our answer wrong. Remember that, integers do not consist of a fractional number. Positive integer can just be said as the set of natural numbers. We cannot find the largest positive integer.