Mathematical knots use endlessly slippery and stretchy rope. Most real knots operate on friction one way or another. Anyway, as a more direct answer to your qu

Mathematical knots use endlessly slippery and stretchy rope. Most real knots operate on friction one way or another. Anyway, as a more direct answer to your question, mathematical ropes use a single loop of rope. By definition the only one that can be tied this way (without breaking the rope) is the unknot. There are several different real knots that can be tied from an unbroken loop of rope.