Question

Prove: [m^2 = n^2] iff [(m = n) or (m = -n)].

ugh ....

Answer 1

to prov a biconditional you split it into its conditional parts and prove

Answer 2

p <-> q

p -> q AND q -> p

Answer 3

?

Answer 4

isn't it obvious.

Answer 5

m^2-n^2=(m-n)(m+n)=0
=> m=n or m=-n

Answer 6

that is p->q

Answer 7

lol ... thats what I thought; why prove the obvious :)

Answer 8

ahh, diff of squares .....

i keep trying tog o to basic with this stuff and prove that counting exists .....

Answer 9

you got q->p?

Answer 10

lol .... im still working on if (amistre64) then (exist)

Answer 11

im thinking contradiction or contraposition in that one

Answer 12

(m=n or m=-n) -> (m^2 = n^2)

If (m^2 ≠ n^2), then (m≠n and m≠-n)

then follow as before

Answer 13

unless there is something glaringly obvious that I am missing

Answer 14

proof by contradiction would be in line with the previous proof tho and might be simpler

Answer 15

if (m=n or m=-n) then (m^2 \(\ne\) n^2)

Answer 16

i hate proofs by contradiction

Answer 17

why can't you just say if m=n, then m^2=n^2
and
why can't you just say if m=-n, then m^2=(-n)^2=n^2
is that just too easy?

Answer 18

if
\[m^2=n^2\iff m^2-n^2=0\iff (m+n)(m-n)=0\] and then it is an openstudy problem

Answer 19

satellite cheated off me

Answer 20

i think we have to do the books method of splitting the hairs

Answer 21

lets ban him ;)

Answer 22

this is one direction for sure. i just woke up no banning me! i can't even see straight yet

Answer 23

i'm gonna type 525325235 for the amout of hours of suspension

Answer 24

you would be doing me a favor. i have at least 4 hours of work to do before i leave the house

Answer 25

lol

Answer 26

other direction is trivial. if
\[m=n \text { then } m^2=n^2\] and if
\[m=-n \text { then } m^2=(-n)^2 = n^2\]

Answer 27

omg cheater

Answer 28

did you write that? ok i cheated, but you have to admit it is the obvious thing to write. what else?

Answer 29

i didn't put in pretty latex though so i guess i will give you some cool points

Answer 30

oops that is what you wrote above isn't it? well lets see...
you could always take the log , use a some property, and then exponentiate...

Answer 31

I proofed by contradiction on the 2nd one :)

Answer 32

if i don't get to work i am going to hate myself by noon. time to get off the computer.
@amistre i hate proofs by contradiction. but why now?

Answer 33

don't go to work

Answer 34

working for free is funner

Answer 35

so you can stay with us

Answer 36

if (m=n or m=-n) then (m^2 ≠ n^2)

(m+n)(m-n) = 0

m^2 +mn -mn -n^2 = 0

m^2 - n^2 = 0

m^2 = n^2

Answer 37

that should annoy your teacher sufficiently

Answer 38

yay!!

my proofs tend to be more socratic :)

Answer 39

lol

Answer 40

having fun?

Answer 41

always and for never