Problem 39
Question
Is there a smallest integer? If so, what is it?
Step-by-Step Solution
Verified Answer
Answer: No, there is no smallest integer.
1Step 1: Understand integers
Integers are whole numbers and their opposites. The set of integers can be written as {…, -3, -2, -1, 0, 1, 2, 3, …}. Both positive and negative whole numbers are included in this set.
2Step 2: Identify what it means to be the smallest integer
To be the smallest integer, a number must be smaller (less) than all the other integers. For example, if there were a smallest integer, that number would have no other integer less than it.
3Step 3: Check for the smallest integer
Let's assume there is a smallest integer represented by the letter "a." Now, consider the integer "a-1." Since "a-1" is an integer and smaller than "a", our initial assumption that "a" is the smallest integer is not correct, which means there is no smallest integer.
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