I feel aggravatingly close to the answer to this one, but have caved in. Using ~ for "is equivalent to" A given question reads: Given that f(x) ~ 3 - 5x + x^3, show that the equation f(x)=0 has a root x = a, where a lies in the interval 1 < a < 2. Clearly asking for the answer here would be more than a little insulting. What I want to know is why it is necessary to use equivalence rather than equality at the beginning. Many thanks.