For example, the subgroups of Z 6 are {0}, {0, 2, 4} and {0, 3}—the trivial subgroup, the multiples of 2, and the multiples of 3. In the group D 6 , rotations form a subgroup, but reflections ...

Multiplication is commutative too: 314 x 159 = 49,926 = 159 x 314. On the other hand, subtraction is not commutative: 314 - 159 = 155, which is not the same as 159 - 314. Nor is division ...

Several fields of mathematics have developed in total isolation, using their own ‘undecipherable’ coded languages. In a new study published in PNAS, Tamás Hausel, professor of mathematics at ...