Question

if x^2 > 0, then x < 0.
Is that statement true or false?

Answer 1

what do you think ?

Answer 2

x>0 or x<0

Answer 3

x<0

Answer 4

Can you find a counterexample?

Answer 5

-1

Answer 6

It says if x^2 > 0, then x < 0.

So if you can find an x>0 such that if x^2 > 0, then that DISproves it, hence it is false.

Answer 7

oh wait. nevermind -1*-1 = 1

Answer 8

-1 fits the definition... what about something that works in the first part but not the second?

Answer 9

Note, however, that the reverse is not true: finding an example for which the statement is true does not PROVE that it's true IN GENERAL.

But finding an example that proves IT'S FALSE does prove that it's NOT TRUE in genera.

Answer 10

2

Answer 11

So what does that tell you? is it true or false?

Answer 12

Pretty sure it's false. be> 0, or 4 >0, then 4 < 0???

Answer 13

because 2^2 > 0

Answer 14

Exactly. :)

Answer 15

What if x has a complex value like 2i ?

Answer 16

WOOOT THANKS DEBBIE

Answer 17

x = -2, x^2 =4
x =2 , x^2 =4
x=2i, x^2=-4

Answer 18

just no.

Answer 19

but which is greater? 2i or -2i? also, is either of these greater or less than 0?

Answer 20

greater

Answer 21

can't compare complex numbers... only their moduli!

Answer 22

so?..

Answer 23

@pgpilot326
Equal but opposite. and when both are squared (-2i)^2 or (2i)^2 the result is still -4 which
is less than zero. The drawing shows their relationship to zero, I will let you decide which one is less than or greater than zero :)


l

Answer 24

1+i or 1 - i?

Answer 25

besides is 2i >0? if so, is -2i>0? can both be?

Answer 26

not really?