Elite QandA


What does it mean when a set is closed under addition?


  1. What does it mean when a set is closed under addition?
  2. Is addition closed under addition?
  3. What does the sum is closed mean?
  4. Is sum of closed sets closed?
  5. What does sum of subspaces mean?

What does it mean when a set is closed under addition?

A set of whole numbers is closed under addition if the addition of any two elements produces another element in the set. If an element outside of the set is produced, then the set of whole numbers is not closed under addition.

Is addition closed under addition?

Closure property holds for addition, subtraction and multiplication of integers. Closure property of integers under addition: The sum of any two integers will always be an integer, i.e. if a and b are any two integers, a + b will be an integer.

What does the sum is closed mean?

That means if the sum of these two functions evaluated at one is also equal to zero. So in general, when we come together to functions, the sum is closed.

Is sum of closed sets closed?

now xnk→x which means subsequence bnk→x−a converge,since B is closed,x−a∈B ,hence x=a+b∈A+B,which means the sum is closed.

What does sum of subspaces mean?

The sum of two subspaces U, V of W is the set, denoted U + V , consisting of all the elements in (1). It is a subspace, and is contained inside any subspace that contains U ∪ V . We can also think of U + V as the intersection of all (typically infinitely many) subspaces containing both U and V .



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