Final answer:
The terms 'older than' and 'two times older' in math are used to compare ages, where 'older than' indicates a simple comparison and 'two times older' signifies a doubling relationship between ages.
Step-by-step explanation:
In mathematics, when we say something is older than another, we are comparing two values where one is greater in age than the other. The phrase two times older, on the other hand, implies a proportional relationship where one value is double the age of another. For example, if person A is 30 years old and is said to be two times older than person B, then person B would be 15 years old, since 30 is two times 15. It is important to understand these phrases as they define the relationships and comparisons between numbers or quantities in mathematical equations and word problems.