5 ms·
Step 9 doesn't work because it introduces a third person, and so fails to demonstrate S(2)
by smallnamespace 6y ago
Step 9 doesn't work because it introduces a third person, and so fails to demonstrate S(2)
- coldtea 6y agoIsn't it Step 4, which uses as a premise what the whole thing is supposed to prove? "in every group of k people, everyone has the same age" You can't use your conclusion in your assumption!
- phepranto 6y agoThat's the way induction works. Assume the statement is true for n Deduce that it then must be true for n+1 Prove it for n=1 Now it's proven for every n
- NieDzejkob 6y agoYou might want to read the section "A Brief Review of the Principle of Induction".
- deleted 6y ago[deleted]
- MauranKilom 6y agoPlease take a look at the principle of induction that is explained on that page. In short: You fix k and assume that S(k) holds. If you can show that this always implies that S(k+1) holds, all you need is a base case (e.g. S(1) being true) to "recursively" prove that S(n) holds for all n >= 1 (or whatever your base case was). Here the fault is that the induction step (proving S(k+1) from S(k)) requires k >= 2 but only specifically S(1) was proven.
- azundo 6y agoNo, not quite, the conclusion is that given a group of k people where all people have the same age, then a group of k+1 people also must have the same age. Since we know that in a group of 1 all k people have the same age, then if the proof held then a group of 2 people would have the same as well, then 3, etc. This is a common tactic in induction, you make an assumption, prove that if true it implies a general result, and then give an explicit case where the assumption holds, proving the general result.
- Ericson2314 6y agoThis is easier to understand in constructive type theory. You can't pattern match on `k` to recur, but you can pattern match on `succ(k)` to recur on `k`. Even when doing classic logic, I start with my constructive intuition and the sprinkle in the continuation-passing-style spooky magic when needed to get back the classical craziness. Everyone should learn constructive first.
- kerkeslager 6y agoYou're right if we were speaking normal English, but "assuming" doesn't mean the same thing in math jargon. In math, you would say, "Assuming A, then B", to mean, "If A is true, then B is true." It's way more confusing than simply "If A, then B", and I'm not sure why the wording hasn't fallen out of favor, but that's what it is.
- OJFord 6y agoIn what way is that different from 'normal English'?
- dlkf 6y agoI don't know why you're getting downvoted, afaict 9 is the problem.
- inimino 6y agoPerhaps downvoted for spoiling the problem? Some people review the comments before looking at the article.
- deleted 6y ago[deleted]
- nathanwh 6y agoTFA will inform you of this though, it's intended to be a game of reasoning. Posting the answer is spoiling the fun for people who read the comments first
- vages 6y agoWhy isn't there a mechanism for hiding spoilers in your comments? I came to the comments to check whether my guess was right (it wasn't), and I'm very glad for the spoiler.
- Thorrez 6y agoYou don't need to come to the comments to check your guess, the website lets you check your guess yourself by clicking on the step. > See if you can figure out in which step the fallacy lies. When you think you've figured it out, click on that step and the computer will tell you whether you are correct or not, and will give an additional explanation of why that step is or isn't valid.
- deleted 6y ago[deleted]
- thaumasiotes 6y ago> it's intended to be a game of reasoning. Posting the answer is spoiling the fun for people who read the comments This is a very common example in math classes, though in my experience usually presented as a proof that "all horses are the same color".
- jhanschoo 6y agoNote that Step 9 can be read as introducing an entity that is known to exist, or introducing a variable to be universally quantified over. It isn't until Step 13 that we see that Step 9 should be read as the former.