(Notice that sum of two knots will be different if you cross the strands.)
It is interesting to look at a knot and ask, "Are there 2 simpler knots that can be added together to produce this knot?" If the answer is "no", then the knot is a prime knot .
When thinking about prime knots and knot addition, the zero knot plays a role very much like the number 1 plays when you think about prime numbers and multiplication.
What else do prime knots and prime numbers have in common? How are they different?
When you add the zero knot to another knot, the knot is not changed. When you multiply a number by 1, the result is always the same number you began with. If you remove, or subtract a copy of the zero knot from a knot, you haven't really changed it. Similary, dividing a number by 1 leaves that number unchanged.
