Recently in class we have learned how to create the number systems and have just defined the definitions of rational Null sequences and Cauchy sequences but with $- 1/k \leq x_i \leq 1/k$ terminology instead of $\epsilon$ and the use of absolute value.
For many of the proofs such as the sum of two null sequences being null, I’d like to use the triangle inequality as it is what I know from real analysis.
As I am working with the rationals, I can’t assume what we know about the Real numbers yet and so is it safe for me to use $|x_i|\leq 1/k$ when doing the proofs or is that incorrect terminology? It would make things so much easier.