> If you say two knots are equivalent, in mathematics, that means they are equal, one and the same. As far as I know a knot is a continuous embedding of S^1 in

> If you say two knots are equivalent, in mathematics, that means they are equal, one and the same. As far as I know a knot is a continuous embedding of S^1 into R^3. Equal means exactly same subset of R^3. Equivalence of knots means that there is a suitable ambient isotopy between the nots (I just looked this up in wikipedia: https://en.wikipedia.org/wiki/Knot_theory#Knot_equivalence https://en.wikipedia.org/wiki/Knot_theory#Knot_equivalence). So equality is a much stronger criterion than equivalence. So 'equal => equivalence', but the other direction 'equivalence => equal' trivially does not hold (just apply some transition in R^3; these knots are equivalent but not equal).