My first solution is
Let
##S = \{x_1, x_2, x_3, ..., x_n\}##
##T = \{2x_1, 2x_2, 2x_3, ... 2x_n\}##
##T = 2S##
Therefore, ##inf T = inf 2S = 2inf S = 2M##
May someone please know whether this counts as a proof?
My second solution is,
##x ≥ M##
##2x ≥ 2M##
##y ≥ 2M## (Letting y = 2M)
Let...