The assumption that the case holds for n while the goal is to show the case holds for n+1. It is not well worded to make clear the intent of making an assumptio

The assumption that the case holds for n while the goal is to show the case holds for n+1. It is not well worded to make clear the intent of making an assumption about modal possibility. However, to see it as begging the question requires imposing a statement of modal necessity that simply isn't there.