I'm trying to understand the construction of the real numbers using Cauchy sequences. I get that not all rational Cauchy sequences converge to a rational number, however, how do we know that the number they do converge to is real? Is there something I'm missing or do you need to prove that all rational Cauchy sequences converge to a real?
2026-03-28 20:13:33.1774728813
Proof that all rational Cauchy sequences converge to real
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