Irrational numbers have an infinite number of non-repeating decimals, the only exact way to represent them is symbolic
Yes of course, by definition, but some implementations have real numbers which are only limited by the size of memory, right? Not to get too off topic but the fact that real numbers can only be represented as a process which produces them given infinite computational power really does give a lot of merit to the finitist position. Either that or a rejection of mathematical objects as the fundamental building block of mathematics rather than processes.