Definition
Non-example
A non-example is something that does not fit a mathematical idea’s defining rules.
What it means
It shows where an idea stops. Check the rules for the idea, then point to the rule the object breaks. A useful non-example differs for a mathematical reason, not just because its colour, size, or position changed.
Remember it
An example passes every rule; a non-example hits at least one stop sign.
Example
A square must have four equal sides and four right angles. A 3 cm by 5 cm rectangle has four right angles but not four equal sides, so it is a non-example of a square.
Watch for
A counterexample is a special non-example used to show that a statement is false; not every non-example disproves a statement.
Common mix-up
Changing only decoration does not make a useful non-example if all defining conditions still hold.
Exact meaning
A non-example is an object, case, or result that fails at least one defining condition of the concept being studied.