How can you analogize mathematical induction to dominoes falling, if some domino can fail to topple? [closed]
Closed as not constructive by Peter Taylor on Jan 5, 2022 at 10:00
This question cannot be answered in a way that is helpful to anyone. It's not possible to learn something from possible answers, except for the solution for the specific problem of the asker.
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This analogy doesn't convince me, because what if some domino (after b, the base case) fails to topple? In real life, a domino can remain standing upright if it got placed too far apart from the previous domino — or if the previous domino didn't hit this steadfast domino with sufficient force (to topple this steady domino).
David Gunderson, Handbook of Mathematical Induction (2010), pp 4-5.
It is an analogy and the essential point is that each step leads to the next, just like, in case of dominoes (when they work), each one topples the next.
You have focused upon a case where the analogy breaks. It is a good idea to detect such cases and maybe it makes the analogy less useful for you, if the parts where the analogy does not work are, for you, essential features of the phenomenon. This is okay.
Hopefully you have mastered the concept while thinking through the matter; if so, the analogy has served its need, and if not, you should solve some problems and build more intuition.
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