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, •).
The natural numbers with addition form a magma. Because the set of natural numbers is written as and addition is written as the magma is written as . 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 and multiplication (in abstract mathematics) is written as the magma is written as . The name of the magma would be "The integers under addition".
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 . It can be shown that the is a magma.