I mean when talking about real numbers this way, we mean numbers that can only we represented as compositions of periodic digits, or worse, transcendental numbe

I mean when talking about real numbers this way, we mean numbers that can only we represented as compositions of periodic digits, or worse, transcendental numbers which lack even periodicity. However, unless you do Numerics, you probably choose a different representation, for instance as series. This is precise and there is a choice of Computer Algebra Systems available for that. In fact Algebra has very deep connections to pen and paper geometry. Apart from that... Due to the increased use of statistics, the postulates of CS might shift. One example being CAP theorem.