Remark
14
[1X1](Solved on 2022-10-11) The variable \(x\) , which is quantified in a part of a formula, is again free if it is reused in another piece of the formula; this is syntactically permissible but makes the formula less readable, as in this example that uses the language of set theory
\[ A⊆ {\mathbb {N}}∧ x∈ {\mathbb {N}}∧ x≥ 4 ∧ (∀ x∈ A,x≤ 10) \]
which should be written as
\[ A⊆ {\mathbb {N}}∧ x∈ {\mathbb {N}}∧ x≥ 4 ∧ (∀ y∈ A,y≤ 10) \]
renaming the variable inside the part where it is quantified.