Question 366143
Let n = first number (which is an integer)


So {{{n+1}}} is the next consecutive number.



Now add up the two numbers to get {{{n+(n+1)=(n+n)+1=2n+1}}}



Since n is an integer, {{{2n}}} is even (since 2 is a factor). So {{{2n+1}}} is odd.



So any odd number can be expressed as the sum of two consecutive numbers.



So to answer the question "what name is given to all the numbers that can be expressed as the sum of two consecutive numbers?", the answer is the set of odd integers.