"if 2 is not equal to 5"

[Genady]

Why the professor says "if"?

 

[timo]

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.

[Genady]

This part is correct:

9 minutes ago, timo said:

for some other reason

😉

He has a mathematical reason to say "if".

[Genady]

Hint.

Here

he is asking, "5 can be equal to 2? 5 can't be equal to 2?"

[joigus]

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

[Genady]

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

[joigus]

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

[Genady]

19 minutes ago, joigus said:

I added a spoiler.

Me too.