## Math Symbols The Most Valuable and Important Symbols For Set Notation In Use: "PROPER Subset (left) to Set (right)"

Math Symbols: . . . why math symbols are used . . .

Symbols are a concise way of giving lengthy instructions related to numbers and logic.

Symbols are a communication tool. Symbols are used to eliminate the need to write long, plain language instructions to describe calculations and other processes.

For example, a single symbol stands for the entire process for addition. The familiar plus sign eliminates the need for a long written explanation of what addition means and how to accomplish it.

The same symbols are used worldwide . . .

The symbols used in mathematics are universal.

The same math symbols are used throughout the civilized world. In most cases each symbol gives the same clear, precise meaning to every reader, regardless of the language they speak.

The most valuable, most frequently used Symbols in mathematics . . .

The most important, most frequently used Symbols for Set Notation are listed below.

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Symbols for Set Notation - click description

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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")

The math symbol is equivalent to and is interchangeable with (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.

In contrast, the subset math symbol represents any subset, but not necessarily a Proper Subset. Item (2), above, does not apply when the symbol is used. 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.

Example 1: , Set A:   A = { a , b, c , d}

Set D:   D = { a , c }

. . . Both Set "D" and Set "A" contain the following elements: a, c

. . . All of the elements in Set "D" are also elements of Set "A".

. . . 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 }

. . . Both Set "E" and Set "B" contain the following elements: 9, 11

. . . All of the elements in Set "E" are also elements of Set "B".

. . . 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 }

. . . Both Set "F" and Set "C" contain the following elements: rabbit, cat

. . . All of the elements in Set "F" are also elements of Set "C".

. . . 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.