A mathematical rule can be called many things including a theory. Proofs can prove this theory to be a rule.
Fraction
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The empty set is the set that contains no elements. (It is the empty set, not an empty set, because there is only one of them. It is a unique mathematical object.)
algorithm
A mathematical rule can be called many things including a theory. Proofs can prove this theory to be a rule.
Equations .
sequence
various arrows
It set an example for self-rule.
A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets
Q = {a,b,c}
An equation contains mathematical symbols, such as + - / *. However, there are also other kinds of mathematical symbols (algebra, trigonometry and calculus) which may look different and some of which are words. examples of this may be: cos(x) tan(x) sin(x) to name a few. There are however, more often than not, "standard" (+ - / *) operators in the more advanced mathematical equations to.
In mathematical terms an element may be a member of a set.
A solution set makes a mathematical sentence TRUE.
Fraction
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