Completeness and Baire category (intro)
General · Mathematics
Study notes
Q: Is ℚ complete? Show a Cauchy sequence in ℚ with no rational limit. √2 approximations: 1, 1.4, 1.41, 1.414, ...: Cauchy (terms cluster!). Limit √2 ∉ ℚ: NO rational limit - ℚ INCOMPLETE! ℝ: complete (limits exist!). Baire: ℝ not countable union of nowhere-dense sets!