Question

List the elements in each set. See Example 1. {k|k is an odd integer less than 1}

Accepted Answer

Understand the problem: We need to list all elements of the set defined by $$ \{k \mid k 	ext{ is an odd integer less than } 1\} . $$This means all odd integers $$k$$ such that $$k \u003c 1. $$Recall what odd integers are: Odd integers are integers that can be written in the form $$2n + 1$$, where $$n is $$any integer (positive, negative, or zero). Examples include $$\ldots, -3, -1, 1, 3, 5, \ldots. $$Identify the odd integers less than 1: Since $$k \u003c 1$$, we consider all odd integers less than 1. These are $$\ldots, -5, -3, -1. $$Note that 1 itself is not included because the inequality is strict (less than 1, not less than or equal to 1). List the elements explicitly: Write out the odd integers less than 1 in increasing order, for example, $$\{\ldots, -5, -3, -1\}. $$Since the set includes infinitely many negative odd integers, it is an infinite set extending indefinitely in the negative direction. Summarize the set: The set $$\{k \mid k 	ext{ is an odd integer less than } 1\}$$ contains all odd integers less than 1, which are all negative odd integers and zero is excluded because it is not odd.

List the elements in each set. See Example 1. {k|k is an odd integer less than 1}

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Key Concepts

Set-builder Notation

Odd Integers

Inequalities and Number Line