Since Montessori classrooms emphasize non-competitiveness, how are students adequately prepared for real-life competition later on?

Montessori classrooms emphasize competition with oneself: self-monitoring, self-correction, and a variety of other executive skills aimed at continuous improvement. Students typically become comfortable with their strengths and learn how to address their weaknesses.  It is a healthy competition in which all contenders are content that they did their best in an environment with clear and consistent rules.