How to Prove All Dominoes Fall in an Infinite Arrangement

What is a statement? A statement is a declarative sentence that expresses a fact, opinion, or viewpoint about a particular subject. It is typically composed of a subject, predicate, and an expression of opinion. Statements typically serve to make a point, provide an explanation, or offer a suggestion. Statements can also be used to convey an emotion or action. For example, "I love you" is a statement of emotion. Statements are used in a variety of communication contexts, such as in essays, speeches, conversations, and other forms of communication.

Induction Hypothesis:

Assume that the statement holds true for any arrangement of n dominoes.

Inductive Step:

Consider an arrangement of n + 1 dominoes. Since the first three fall, and the nth domino falls when the (n + 3)rd domino falls, all n + 1 dominoes fall.

Conclusion:

By strong induction, it is proven that all dominoes fall in an infinite arrangement of dominoes if you know that the first three dominoes fall, and that when a domino falls, the domino three farther down in the arrangement also falls.

← Exciting insights into linear nonhomogeneous recurrence relations The impact of climate change on coral reefs →

More Posts: