EDB — 29M

6.3 Supremum and infimum[29M]

Let’s first review the characterizations of the supremum and infimum in \(ℝ\), as seen in Sec. [1YY]↺↻ (or in Chap. 1 Sect. 5 in the notes [ 3 ] ). Let \(A⊆ ℝ\) be a non empty set.

Combining the previous results, we get the result already seen in [22S]↺↻ Often the above definitions and properties are used in this form.

Exercises

Let \(I,J\) be generic non-empty sets. See definitions in Sec. 6.3

Exercises

1. [0B6]↺↻

2. [0B7]↺↻

3. [0B9]↺↻

4. [0BC]↺↻

5. [0BF]↺↻

6. [20P]↺↻

7. [20J]↺↻

8. [20Y]↺↻