Again, I don't disagree with any of this. The argument advanced by the OP is that floating point numbers are not intuitive to use for the general public because

Again, I don't disagree with any of this. The argument advanced by the OP is that floating point numbers are not intuitive to use for the general public because they don't work like the unique complete ordered field up to isomorphism. All I'm saying with the cardinality argument is that because real numbers are fundamentally unlike integers, obvious methods of doing things won't work, and we are stuck (at least for the time being) with leaky abstractions. I make no claim about the existence of better/more intuitive solutions. My only counterpoint is that while the ideas outlined in the paper are certainly valuable, I don't think the framework is mature enough to replace the default representation for real numbers in a programming language like Java, at least not without further work and/or proof that it can be adapted to a more general setting without disastrous performance decay. > But, starting from a definition of the reals as a Cauchy sequence... I trust that what you're saying is true, but I'm not familiar with that topic, I'm sorry. Thanks for sharing the paper.