Medical Surveys And Mathematical Induction

Medical surveys such as smoking causes cancer are not supported by mathematical induction. According to mathematical induction:

If Q is a set of integers such that

1. 1 belongs to Q
2. n belongs Q implies n + 1 belongs then
3. all integers greater or equal to 1 belong to Q.

Let us make a set of smokers. Suppose one smoker has cancer. It cannot be shown that n or n+1 smokers have cancer.

The intent of this post is not to encourage smoking but to show how mathematical induction works.