Final answer:
The theorem best proved with mathematical induction is a proposition about all natural numbers. This method is used to establish the truth of a given statement for all natural numbers by confirming it for the first number and then for every subsequent natural number by assumption. Correct option is d) A proposition about all natural numbers.
Step-by-step explanation:
The kind of theorem that is best proved with mathematical induction is d) A proposition about all natural numbers. Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers. It consists of two steps: The base case, where the statement is proven for the first natural number (usually 1), and the inductive step, where one proves that, if the statement holds for some natural number n, then it also holds for n+1. By proving these two steps, one can logically conclude that the statement is true for all natural numbers.
Propositions concerning universal statements or statements involving a conditional form, such as 'If p then q', can sometimes be proven using mathematical induction if they apply to the natural numbers. However, induction is not suitable for statements about all real numbers, existential statements, or any other context where an infinite number of non-discrete steps or elements are involved.