Understanding how order is defined and preserved in ℝ
If (aₖ) ~ (aₖ') and (bₖ) ~ (bₖ'), and aₖ < bₖ eventually, then aₖ' < bₖ' eventually.
Both green sequences converge to 1.5, both red sequences converge to 0.8. Since 1.5 > 0.8, eventually ALL green points are above ALL red points, regardless of which representative we choose.