Question

Why can't "If x^2 = y^2, then x = y" be inferred from the following statement: "If x = y, then x^2 = y^2"?

Answer 1

it can

Answer 2

Because with taking a square root you have a plus/minus ambiguity?

Answer 3

because for example
\[(-3)^2=3^2\] but \[3\neq -3\]

Answer 4

because x^2 has two root, +x and -x
similarly y^2 has two roots, +y and -y

Answer 5

Exactly^^

Answer 6

so if i know the square of my number is 9, i do not know that my number is 3

Answer 7

thats just circular reasoning ;)

Answer 8

an equivalent statement would be
if x^2 <> y^2, then x<> y

Answer 9

"<>" is not equal