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in this supplementary video Id like to talk a bit about the relation between dedicate cuts and now our everyday representation of real numbers as infinite decimals and furthermore Id like to talk about binary expansions of real numbers since well be dealing with those when we talk about the diagonalization argument whenever we do a computation involving a real number we most certainly do not think of these real not resist Dedekind cuts or even as equivalence classes of Cauchy sequences what we do is we think of these as infinite decimals that is we dont think of the square root of two as a subset of the rational numbers with this predicate what we do is we think that square root of two as this infinite decimal expansion which we would always truncate at some location depending upon what level of accuracy we need for a computation so the question Id like to talk about in this video is how we might think of converting between these two representations between this very theoretical