Final answer:
The term that describes the property being true for n = k + 1 is the 'inductive step' in mathematical induction, where showing this step, along with the base case, can prove a statement for all natural numbers.
Step-by-step explanation:
The term used to describe the property being true for n = k + 1 is the inductive step. This is part of the process of mathematical induction, which is a method of proof used to establish that a given statement is true for all natural numbers. The process starts with the base case, where the property is shown to be true for the initial value. The inductive hypothesis assumes that the property is true for some arbitrary case n = k. Then, the inductive step involves showing that if the hypothesis is true for n = k, it must also be true for n = k + 1.
By demonstrating that the base case is true, and that the truth of the proposition for an arbitrary n = k implies the truth of the proposition for n = k + 1, you can conclude that the proposition is true for all natural numbers. This form of reasoning is a key part of inference termed inductive reasoning, not to be confused with deductive reasoning where the conclusion follows necessarily from the premises.