Inductive Hypothesis

An inductive hypothesis is an assumption made during a logical or mathematical proof, especially when proving a statement for all natural numbers. It involves assuming that a particular statement is true for some arbitrary case (say, for a number \( n \)) to then show that, based on this assumption, the statement also holds for the next case (\( n+1 \)). This step helps establish the truth for all cases in a sequence. It's a crucial part of mathematical induction, serving as the foundation for building a general proof from specific, verifiable steps.