Methodical bases of continuity in training to the mathematician

The analysis of a primary and secondary school maths teaching continuity problem shows that it remains one of the most actual and demanding further researches problem nowadays. The author considers that the continuity principle is obligatory for perfection of all methodical system in training of students. The correct understanding of continuity can benefit at the organisation of all training process and its separate stages at school, deeper understanding of a continuity problem can become the serious tool in methodical researches.