Answer to Question #177238 in Real Analysis for TUHIN SUBHRA DAS

Question

Which of the following statements are true and which are false? Justify your answers with 

a short proof or a counter-example.

i) If 

x

and 

y

are real numbers such that 

x < y,

then

x^2 < y^2.

Answer 1

This is a false statement. To see this, suppose that x=-3 and y= -2. We have that $9= (-3)^2 > (-2)^2 = 4$