Technically limits work with Rational Numbers too, so that isn’t an unique property either
No, they don’t; that’s precisely the point. There are Cauchy sequences of rational numbers which don’t converge to any rational number. For an example, simply take the sequence whose nth term is the decimal expansion of pi (or your favorite irrational number) carried out to n digits.
No, they don’t; that’s precisely the point. There are Cauchy sequences of rational numbers which don’t converge to any rational number. For an example, simply take the sequence whose nth term is the decimal expansion of pi (or your favorite irrational number) carried out to n digits.
Noted and corrected.