In an graph, the number of vertices with odd degree is even. We have now seen several examples of mathematical proof, and it's time to investigate what they all have in common. All mammals have hearts All mammals thus far observed have had hearts. All horses are mammals All horses thus far observed have been mammals. Every horse has a heart.
Every horse has a heart.
Note that the difference is not the conclusion, but rather the relation between the premises and the conclusion. We now look at a technique of mathematical proof called mathematical induction. Gauss' formula for the sum of consecutive integers. The second step in this example is a bit more formal than in the postage example, but the principle is the same. Therefore, if the first equation is true, then the second must be true as well.