Including or excluding wrong integers at boundaries
"The Boundary Blunder"
The Mistake in Action
List the integers satisfying $-2 < x \leq 3$
Wrong: $-2, -1, 0, 1, 2, 3$
Why It Happens
Students include -2 even though the $<$ symbol means it's not included, or they may miss that 3 is included because of $\leq$.
The Fix
Check each boundary carefully:
- $-2 < x$ means $x$ is greater than $-2$, so $-2$ is NOT included
- $x \leq 3$ means $x$ is less than or equal to 3, so 3 IS included
Integers in $-2 < x \leq 3$: $-1, 0, 1, 2, 3$
(5 integers, not 6)
Spot the Mistake
Can you identify where this student went wrong?
List integers in $-2 < x \leq 3$
$-2, -1, 0, 1, 2, 3$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: