Use mathematical logic to write the next sentence : For all positive x between 0 and 1, x squared is smaller than x

Question

I am trying to write the sentence

Like this : ∀x((x<1)∧(x>0))→∀x((x^2)<x)

Is there any error here, or is it a suitable solution to the question ?

Answer 1

You should not have the second $\forall x$. $x$ has the same value throughout the statement. Some demand there be a set of parentheses around the whole scope of a quantifier. If you do, you should have a set around the whole implication.

Answer 2

Thank you everyone, the statement is false, informative comments and answers As I understand this is the right way you do it : ∀x(((x<1)∧(x>0))→((x^2)<x))