No.
The set of even numbers is closed under addition, the set of odd numbers is not.
no
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
Let + (addition) be a binary operation on the set of odd numbers S. The set S is closed under + if for all a, b ϵ S, we also have a + b ϵ S. Let 3, 5 ϵ the set of odd numbers 3 + 5 = 8 (8 is not an odd number) Since 3 + 5 = 8 is not an element of the set of the odd numbers, the set of the odd numbers is not closed under addition.
No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.
Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
You can't. Adding any two odd numbers always gives an even number, which is not a member of the set of odd numbers.
The set of all odd numbers. 1+1=2
The sum of the first 500 odd counting numbers is 250,000.
That is correct, the set is not closed.
None of them. All counting numbers are either odd or even.
None. All counting numbers are even or odd.