Complete space

A complete space in mathematics is a type of space where every Cauchy sequence (a sequence where the elements get arbitrarily close to each other) converges to a point within that space. In simple terms, it means there are no "holes" or gaps; sequences that should settle somewhere actually do. This property ensures the space is well-behaved and predictable, which is important for analyzing functions and limits. Examples include the real numbers with standard distance, which are complete, whereas rational numbers are not, because some sequences of rationals approach irrationals outside the rationals.