What does closed under addition mean?
Understand the Problem
The question is asking for the definition of the mathematical concept 'closed under addition', which typically refers to a set of numbers that, when any two elements are added together, the result is also an element of that set.
Answer
A set is closed under addition if the sum of any two elements in the set is also an element of that set.
The answer is that a set is closed under addition if the sum of any two elements in the set is also an element of that set.
Answer for screen readers
The answer is that a set is closed under addition if the sum of any two elements in the set is also an element of that set.
More Information
Closure under addition is a fundamental concept in algebra and number theory. It ensures that performing addition on elements within a set will not result in elements outside the set.
Tips
A common mistake is to assume that closure under addition applies universally to all operations like multiplication or subtraction without checking.
Sources
- Using the closure property for addition of whole numbers, integers - study.com
- Elementary set theory - What does 'closed under ...' mean? - math.stackexchange.com
- Closure Property - Addition, Multiplication, Formula, Examples - cuemath.com
