What does order mean in math term?

Answer 1

There are more than a math term that use "order". They are:

• the cardinality or the number of elements in the set in group theory.
• the smallest positive integer n such that aⁿ = identity.
• a sub-ring of the ring that satisfies some conditions:

1. That given ring is a ring which is finite-dimensional algebra over the rational number field.
2. The sub-ring spans over the rational root field, such the product of rational number field and the sub-ring is the ring.
3. The sub-ring is the positive-integer lattice of the ring.