Magma (mathematics)

Inmathematics,amagmais kind ofalgebraic structure.It is asetwith abinary operationon 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 asX) and the binary operation a label (such as •). Then we give the magma the label (X,•).

Examples

Thenatural numberswithadditionform a magma. Because the set of natural numbers is written as$\mathbb {N}$and addition is written as$+$the magma is written as$(\mathbb {N},+)$.The name of the magma would be "The natural numbers under addition".

Theintegerswithmultiplicationform a magma. Because the set of integers is written as$\mathbb {Z}$and multiplication (in abstract mathematics) is written as$\cdot$the magma is written as$(\mathbb {Z},\cdot )$.The name of the magma would be "The integers under multiplication".

Thereal numbersunderdivisiondonotform a magma. This is because numbers cannot be divided by 0. A binary operation requires thatanytwo 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$\mathbb {R} ^{*}$.It can be shown that the$(\mathbb {R} ^{*},\div )$is a magma.