Definition
Generalisation
A generalisation extends a noticed pattern or relationship to every case in a stated range.
What it means
Examples can reveal a pattern, but a generalisation reaches farther. It says which cases the rule covers. A sound generalisation also needs a reason showing that no covered case has been missed.
Remember it
Spot the pattern, state the range, justify every case.
Example
After checking 3 + 5 = 8 and 7 + 9 = 16, you might generalise that the sum of any two odd whole numbers is even. The reason is (2a + 1) + (2b + 1) = 2(a + b + 1).
Watch for
Several matching examples support a conjecture, but examples alone do not prove that a generalisation holds for every case.
Common mix-up
A pattern guess says what may continue; a justified generalisation says where it holds and why.
Exact meaning
A mathematical generalisation states that a pattern or relationship holds for every case in a specified domain, not only for the examples used to notice it.