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Chapter 2: Problem 39

Is there a smallest integer? If so, what is it?

Short Answer

Expert verified
Answer: No, there is no smallest integer.

Step by step solution

01

Understand integers

Integers are whole numbers and their opposites. The set of integers can be written as {鈥�, -3, -2, -1, 0, 1, 2, 3, 鈥. Both positive and negative whole numbers are included in this set.
02

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.
03

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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