>>11145039You need to start with a definition of what a knot is mathematically.
A knot is a smooth function from S^1 into R^3. There's an obvious smooth map, i.e. the inclusion map. Then this gives the unknot, a knot with crossing number zero.
In general you define knots up to a sequence of moves and smooth ambient isotopies. So this diagram is just one possible representative from an infinite equivalence class of knots. The issue then becomes that crossing number isn't invariant with respect to the reidmeister moves so you next to look at reduced diagrams, where all crossings in the knot projection cannot be moved away with an ambient isotopy nor a reidmeister move.
