Unlike previous posts, this one precedes the math club meeting. The reason is that we need to tighten some loose ends in our emerging knot theory notation. The first two meetings (I and II) were all about exploring knots and ways to describe them using notations, and we made some impressive strides. But at this stage I need to exercise some authority and steer them firmly in the right direction:
We are going to use I rather than 0 (zero) to denote the identity of composition. Even though 0 is a neutral element for addition, as correctly spotted by the children, using it as the neutral element for composition is not idiomatic. 1 (one) is more standard, for various reason I will not get into here.