Magma (mathematics)

In mathematics, a magma is kind of algebraic structure. It is a set with a binary operation on that set.
A binary operation works by taking two elements from a set (that do not have to be different) and returning some other element of that set.
If we give the set a label (such as "X") and the binary operation a label (such as •). Then we give the magma the label ("X", •).
Examples.
The natural numbers with addition form a magma. Because the set of natural numbers is written as formula_1 and addition is written as formula_2 the magma is written as formula_3. The name of the magma would be "The natural numbers under addition".
The integers with multiplication form a magma. Because the set of integers is written as formula_4 and multiplication (in abstract mathematics) is written as formula_5 the magma is written as formula_6. The name of the magma would be "The integers under multiplication".
The real numbers under division do not form a magma. This is because numbers cannot be divided by 0. A binary operation requires that "any" two elements can be taken from the set (in this case in order) to produce another element from the set. The real numbers without 0 is written as formula_7. It can be shown that the formula_8 is a magma.