Sum of the Natural Numbers Puzzle

This week I discovered one of the strangest results in mathematics I have ever come across. I will explore this in the format of a puzzle and explain what could be thought of as correct answers. So the puzzle is: What is the sum of all the natural numbers. The natural numbers are the positive integers. To clarify this is the sum from 1 to infinity of the natural numbers, as expressed in the sum below. This is a slightly weird one, because depending on how you define some aspects of mathematics, you may receive a strange answer.