Notation: Is $(\Delta x)^2 = \Delta x^2$? I read this in a book and was wondering whether it's valid or not: ![enter image description here]( I thought $\Delta x^2$ would mean 'change in $x^2$', which would be quant...--prophetes.ai

Notation: Is $(\Delta x)^2 = \Delta x^2$? I read this in a book and was wondering whether it's valid or not: ![enter image description here]( I thought $\Delta x^2$ would mean 'change in $x^2$', which would be quantitatively different to $(\Delta x)^2$; no?

This is just notation. It is a typical convention that $\Delta x^2 = (\Delta x)^2$.

You are right that it seems ambiguous, but it is consistent in the calculus literature that I have seen that whenever they write $\Delta x^2$, they mean $(\Delta x)^2$.