3 ms·
Reals numbers give you the property that if a continuous curve is bigger than zero somewhere, and smaller somewhere else, then it must cross the line at a certa
by WilliamLP 17y ago
Reals numbers give you the property that if a continuous curve is bigger than zero somewhere, and smaller somewhere else, then it must cross the line at a certain point. You probably want to say that sqrt(2) has a solution. Without reals you don't have this.
- phaedrus 17y agoI would say that the solution to sqrt(2) is the expansion (to however many finite number of iterations you run it for) of the bits produced by the Turing machine that computes sqrt(2). Sqrt(2) is a computable number, so it exists both in my system and in yours.