Definition
Subset
A subset is one set made only from elements found in another set.
Continue from this idea into connected AXIO math.
Every item from the first set fits inside the second.
Boundary: A subset may be equal to the other set. Use proper subset when the first set must leave out at least one element.
What it means
Check every item in the first set. If each one also appears in the second set, the first set fits completely inside the second. One extra item in the first set is enough to make the subset claim false.
Remember it
Every item from the first set fits inside the second.
Example
Let A = {2, 4} and B = {2, 4, 6}. Both elements of A are in B, so A ⊆ B. Because B also has 6, A is a proper subset of B.
Watch for
A subset may be equal to the other set. Use proper subset when the first set must leave out at least one element.
Common mix-up
A number is an element, not usually a subset: 2 ∈ {2, 4}, while {2} ⊆ {2, 4}.
Exact meaning
Set A is a subset of set B if each element in A can also be found in B. We write A ⊆ B. A set counts as its own subset; a proper subset is missing something that B contains.