"The above principle works because of the fact that every non empty set of positive integers has the least element. In fact it can be proved that the principle of mathematical induction is equivalent to the fact that every non empty set of positive integers has the smallest element"
-The text is from Challenge and Thrill of Pre-College Mathematics published by New Age International Limited.
The part in the statement that i don’t understand is that how is well ordering principle equivalent to principle of mathematical induction. And can the principle of mathematical induction be extended to the negative integers.I am certainly lacking insight over the topic as I am new to it and hence I am confused so I just want to know how the two things relate.