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so what are some examples of numerical invariance for knots in other words for a given not how can we associate with that not a number and today itamp;#39;s going to be a positive integer in such a way that that number only depends on the knot itself and not on the diagram that we use to represent that knot these numerical invariants were going to take a quick survey of include the unknotting number the bridge number and the crossing number and this presentation parallels chapter 3 in colin adams the knot book so the first invariant that weamp;#39;ll meet is called the unknotting number of a knot and we define the unknotting number to be the minimal number of crossings that we need to change in a diagram in order to turn that diagram into the diagram of a nun not so this is the first of three numerical invariance that weamp;#39;re going to see and in each one of them one of the key words in the definition is the word minimal this is whatamp;#39;s gonna make it something which depen