Tuan Topeng

2024-09-28 18:16:14

Today, we're exploring a concept using dominoes, directly connected to mathematical induction. Imagine a row of dominoes. In the first case, we do nothing, and the dominoes remain standing. Nothing happens because no force is applied, and the sequence stays intact.In the second case, we remove the second domino. With one piece missing, the sequence is broken. If we try to topple the dominoes, the flow is interrupted, and the rest won't fall in sequence.In the third case, we topple the third domino instead of the first. Only the dominoes after it fall, while the first and second remain standing.Finally, in the fourth case, we push the first domino. As expected, all the dominoes fall perfectly in sequence, from the first to the last.How does this connect to mathematical induction? Imagine each domino represents a step in a proof. Induction starts with the first step, just like pushing the first domino. If the first step is true and each step depends on the previous one, the entire process follows logically, just like dominoes falling one by one. If a step is missing or we start in the middle, like in the second and third cases, the sequence breaks down. Induction works because the first step is true, and each subsequent step follows. Like the domino effect, once we begin, the entire chain falls in order.

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