Math Symbols
The Most Valuable and Important
Symbols For Set Notation In Use:
"PROPER Subset (left) to Set (right)"
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Background - why math symbols are used. . .
Symbols are a concise way of giving lengthy instructions related to
numbers and logic.
Symbols are an invention, not a discovery. They are a
communication tool. Symbols are used to eliminate
the need to write long, plain language instructions to describe
calculations and other processes.
The most valuable, most frequently used Math Symbols . . .
The most important, most frequently used Symbols for Set Notation
are listed below.
Symbols for Set Notation - click symbol
Symbol for "PROPER (1) Subset (left) to Set (right)" -
D  A means Set "D" is a PROPER Subset of Set "A":
(1)
Every element (without exception) contained in Set "D" is also present in Set "A".
And . . .
(2)
Set "D" cannot be equal to Set "A". (Set "D" must have a smaller number of elements than Set "A")
Example 1:
, Set A: A = {a, b, c, d}
Set D: D = {a, c}
(1) . . .
Both Set "D" and Set "A" contain the following elements: a, c
(2) . . .
Set "D" and Set "A" are not equal. Set "A" contains more elements than Set "D".
Set D is a "Proper Subset" of Set A
D A
Example 2:
, Set B: B = {1, 3, 9, 11}
Set E: E = {9, 11}
(1) . . .
Both Set "E" and Set "B" contain the following elements: 9, 11
(2) . . .
Set "E" and Set "B" are not equal. Set "B" contains more elements than Set "E".
Set E is a "Proper Subset" of Set B
E B
Example 3:
, Set C: C = {cat, bird, dog,
horse, rabbit}
Set F: F = {rabbit, cat}
(1) . . .
Both Set "F" and Set "C" contain the following elements: cat, rabbit
(2) . . .
Set "F" and Set "C" are not equal. Set "C" contains more elements than Set "F".
Set F is a "Proper Subset" of Set C
F C
Note: the elements within a SET/SUBSET can be listed in any order.
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(notice the equal sign at the bottom edge of the symbol is crossed out, indicating the subset cannot be equal to the set). Both symbols mean exactly the same thing: a "Proper" Subset.
represents a subset, but not necessarily a Proper Subset. Item (2), above, does not apply. If this symbol is used, it indicates that the subset (labeled "D" in the example shown above) and the set (labeled "A" in the example shown above) can be equal.