UCLA Olga Radko Endowed Math Circle

11/18/2007: Circle meeting (Dimitri Shlyakhtenko)

Notions of Dimension
What does it mean that a particular set has dimension 1, 2 or 3? How can we tell the dimension of a set? Can sets have non-integer dimension?

We shall discuss these topics on the example of certain subsets of the real line. One of the first problems will be to understand the set of all numbers x in the interval [0,1], for which the digit 5 does not occur in the decimal representation.