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today Iamp;#39;m gonna talk about space-filling curves a very interesting mathematical object that has applications in stock market pricing as well as natural phenomenon such as how a tree evolves so on this slide you see two sets of objects on the left you see three objects a cat a dog and a giraffe on the right hand side you see a set containing also three objects a leaf a bone and a fish how do we know that these two sets are of the same size of course we can count but the mathematical way that we do this is via a correspondence or connection between the objects on the left and the objects on the right so for example the cat likes to eat the fish the giraffe likes to eat leaves and the dog likes to eat the bone so in this way we have a link from each object on the left to each object on the right this is one way and a very important way for us to ascertain that both sets have the same size on this slide I show you two other sets each of which has infinitely many numbers so on the L