Question

Help with easy proof
Prove or disprove :
http://prntscr.com/3h1096

Answer 1

\((2*3) ! \ne 2! 3!\)

\((2+3)! \ne 2! + 3!\)

can this be called a legitimate proof ?

Answer 2

It depends what level of proof your teacher/professor is requesting. If you are used to writing more formal proofs, then I would say no.

However, simply showing a counterexample is a legitimate proof in most cases. I would say you disproved both statements.

Answer 3

its a counter example for disprove
and yes its a legitimate proof

Answer 4

Yep ! how should i set it up for a more formal/elegant proof ?
where should I start... any ideas ? basically I could not think of any other ways to approach this as of now...

Answer 5

if there is a counter example then no need to prove or disprove like in formall,
just say disprove
and here is a counter example

Answer 6

Bswan i think so... counter example is considered a legitimate proof..

Answer 7

only in disprove cases :)

Answer 8

just wondering if there are any other neat ways to think about this...

Answer 9

ofc yes :) we cant say "its ridiculous, so not possible" in a proof lol :P

Answer 10

you mean like real disprove :D
but why to bother ur self with that hah
but i should give it a try , ill check it again
nd tell you

Answer 11

not just for this problem... i want to know in general :) thank you, il wait for your reply :)

Answer 12

counterexample comes to mind

Answer 13

only counter example is the known way for doing these kind of proofs i guess...

Answer 14

one counter is:

(2*5)! = 10.9.8.7.6.5.4.3.2.1

2! * 5! = 5.4.3.2.1 * 2.1

Answer 15

10.9.8.7.6.5.4.3.2.1 =? 5.4.3.2.1.2.1

10.9.8.7.6 =? 2.1, doesnt look promising lol

Answer 16

lol yesss i got counter examples for both (mn)! and (m+n)!
m = 2, n = 3
it should be QED

Answer 17

QED is for when you prove something true.

Answer 18

there is no QED for this proof :)

Answer 19

ooops !

Answer 20

@rational from the beginning, you successfully disproved the statement. What I meant by "more formal" is guiding the reader to your conclusion, not just stating that \(6!\neq2!3!\) but this is purely technical. You have shown the statement is not true by providing a counterexample.

Answer 21

got you :)

\(((2*3)! = 720) \ne (12 = 2!3!) \implies (mn)! \ne m!n!\)
\(((2+3)! = 120) \ne (8= 2! + 3!) \implies (m+n)! \ne m!+n!\)

so the given statements are not true in general

Answer 22

If you're asking whether or not there is a more elegant way, I think not. Elegance is simplicity, and a counterexample is the simplest way to disprove a statement.

However, it is different if you are trying to prove a statement TRUE. In that case, you need a more general approach. That is when you have to think about every possible case.

Here though, you're proving the statement false. So a counterexample will do just fine :)

Answer 23

thanks @dummyguy @BSwan @amistre64 :)

Answer 24

lol and i was thinking about this while washing the dishes to give a reply xD
glad u got it :)

Answer 25

what is this subject ?

Answer 26

number theory...

Answer 27

cool :)