SPP, how do you define real numbers and their decimal representation?

I haven't seen you once define, or engage with anyone who defined real numbers. So answer my question: how do you define real numbers, and their decimal representation? Do you accept the Dedekind cuts definition, the Cauchy sequences definition, or the complete ordered field definition? If not give your own in a rigorous way.

If you don't give a clear answer then I'll assume you're confimring that you're a troll.