Timeline for Why are induction proofs so challenging for students?
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| Nov 26, 2015 at 21:52 | comment | added | Vandermonde | need for another statement to be evaluated first for such to be the case, and if something appears to be time-dependent then it's a collection of statements in disguise -- so that when one uses induction, the assertion is genuinely proven on $\mathbb{N}$ (the completed infinity) as a fait accompli of sorts, whereas real-life implications are typically causal like yours and like the fall of each domino guaranteeing the fall of the next, so that at no (finite) time will one ever witness all the propositions fulfilled. Maybe; it's hard for someone to articulate what it is that throws them off. | |
| Nov 26, 2015 at 21:52 | comment | added | Vandermonde | I love this and remember just this example from the very first page and from section 6.9.2 of here.) As little as people seem to consciously acknowledge it, non-trivial implications in real life are not truth-preserving but rather approximations, and approximations by design aren't transitive (consider the Sorites paradox). Also, something I theorise plays into the difficulty is that logical implication is based on truth values without regard to any notion/impression one may have about causation -- statements are true or false, no | |
| Nov 24, 2015 at 14:34 | comment | added | David E Speyer | @JosephO'Rourke True! I've been learning particle physics recently, and it is striking to me how many things I have to believe how many people got right in order for experimental results to be meaningful. | |
| Nov 24, 2015 at 14:32 | comment | added | Joseph O'Rourke | "I'll be living homeless": Ha! This doesn't undermine your point---perhaps supports it---but in the intersection of particle physics and cosmology, there are some impressively long chains of reasoning, e.g., entertained in the search for dark matter. | |
| Nov 24, 2015 at 14:26 | history | answered | David E Speyer | CC BY-SA 3.0 |