Prove that for any given x R, there is a sequence {gn} of rational numbers which converges to x. You must first construct the sequence {qn}. Then you must prove that {qn} rightarrow x. To construct {qn}, for each n 1, let an = x - 1/n and bn = x + 1/n. Then use the Archimedean property:
Show transcribed image textProve that for any given x R, there is a sequence {gn} of rational numbers which converges to x. You must first construct the sequence {qn}. Then you must prove that {qn} rightarrow x. To construct {qn}, for each n 1, let an = x - 1/n and bn = x + 1/n. Then use the Archimedean property:
