PEAZIT Aha card
Go straight to resources ↓Interval endpoints decide whether boundary values belong
An interval contains every real number between its bounds. ≤ includes an endpoint; < excludes it. Counting integers is not counting all interval members.
| Relation | Meaning |
|---|---|
| A = {x ∈ ℝ: −1 ≤ x < 3} | The left endpoint is included, the right excluded. |
| −1 ∈ A; 3 ∉ A | Check the endpoints separately. |
| A ∩ ℤ = {−1; 0; 1; 2} | There are four integers but infinitely many real numbers. |
One worked example
- A = {x ∈ ℝ: −1 ≤ x < 3}The left endpoint is included, the right excluded.
- −1 ∈ A; 3 ∉ ACheck the endpoints separately.
- A ∩ ℤ = {−1; 0; 1; 2}There are four integers but infinitely many real numbers.
Watch out: Bracket conventions differ between countries. The inequalities are unambiguous; here we count only integers.
Goal, prerequisites and card origin
What you will learn: Decide which values belong to an interval.
What you need first: Inequalities and the number line.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
An interval contains every real number between its bounds. ≤ includes an endpoint; < excludes it. Counting integers is not counting all interval members.