Number Lines and Intervals | Foundations for Calculus Part 3

What does an open circle on a number line tell us? Let's connect inequalities, number-line pictures and interval notation by testing which boundary values belong. We'll build bounded intervals, include the fractions and decimals between the labels, and explain why infinity always uses a parenthesis. Then we'll combine conditions with AND and OR and use union to describe two separate allowed regions. Prerequisites: Comparing positive and negative numbers. Chapters 00:00 Connecting inequalities, number lines and intervals 00:18 Reading the real number line 00:57 Inequality symbols and boundary inclusion 01:33 Combining two conditions with AND 02:12 Testing open and closed endpoints 03:20 Fractions, decimals and the whole interval 04:00 Writing interval notation 04:40 Checking values outside the interval 05:21 Try it: include zero and exclude four 05:48 Solution: the interval [0, 4) 06:27 Unbounded intervals and infinity 07:43 Intervals extending left 08:20 OR and the union of two intervals 09:37 Recap: matching all three representations Additional materials: https://getinfinityinsights.com/