Genady Posted October 21 Share Posted October 21 Why the professor says "if"? Link to comment Share on other sites More sharing options...
timo Posted October 21 Share Posted October 21 The professor is preparing you for the next step where he/she says "and now assume 2 and 5 were any arbitrary value: all steps I did still hold true, so...": "When Tv1 = av1 and Tv2 = bv1: If a!=b then v1 and v2 are not colinear". Either that or for some other reason or for no reason whatsoever. Link to comment Share on other sites More sharing options...
Genady Posted October 21 Author Share Posted October 21 This part is correct: 9 minutes ago, timo said: for some other reason 😉 He has a mathematical reason to say "if". Link to comment Share on other sites More sharing options...
Genady Posted October 22 Author Share Posted October 22 Hint. Here he is asking, "5 can be equal to 2? 5 can't be equal to 2?" Link to comment Share on other sites More sharing options...
joigus Posted October 22 Share Posted October 22 (edited) Spoiler I would assume the professor means we are not in a discrete arithmetic in which 5 = 2 (mod p) for some p. That p would be 3, as 5 = 2 (mod 3) Edited October 22 by joigus spoiler added 1 Link to comment Share on other sites More sharing options...
Genady Posted October 22 Author Share Posted October 22 (edited) 23 minutes ago, joigus said: Spoiler I would assume the professor means we are not in a discrete arithmetic in which 5 = 2 (mod p) for some p. That p would be 3, as 5 = 2 (mod 3) Spoiler He only assumes that vector space is defined over a field. Quotient field mod 3 is as good for this as any. +1 Edited October 22 by Genady Link to comment Share on other sites More sharing options...
joigus Posted October 22 Share Posted October 22 (edited) Spoiler Exactly. Just to correct myself. The p would be any integer multiple of 3, not necessarily 3. And yes, fields is the relevant concept there. I forgot. Sorry, I didn't realise this was under the Teasers and Puzzles section. I added a spoiler. Edited October 22 by joigus spoiler added Link to comment Share on other sites More sharing options...
Genady Posted October 22 Author Share Posted October 22 19 minutes ago, joigus said: I added a spoiler. Me too. Link to comment Share on other sites More sharing options...
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