Is the set N={1,2,3,4,5,.....} closed under addition or not closed under addition? Explain why or why not or show a counterexample. Please help ASAP!!! :(
closed. the set is infinite, and the sum of any two elements is a member of the set.
To determine whether the set N={1, 2, 3, 4, 5, ...} is closed under addition or not, we need to check if the sum of any two numbers from the set also belongs to the set.
Let's take two arbitrary numbers, a and b, from the set N. We'll add them together to see if the result is also in the set.
a + b = (some positive integer) + (some positive integer)
Since the set N includes all positive integers, the sum of any two positive integers will certainly give another positive integer.
Therefore, any sum of two numbers from the set N will still be in the set N. Hence, the set N is closed under addition.
To summarize, the set N={1, 2, 3, 4, 5, ...} is closed under addition because the sum of any two numbers from this set will also be a positive integer, which is included in the set N.