• Journal of Educational Research in Mathematics
• /
• v.25 no.3
• /
• pp.367-379
• /
• 2015

The existence of mathematical objects was considered through diorism which was used in ancient Greece as conditions for the existence of the solution of the problem. Proposition I-22 of Euclid Elements has diorism for the existence of triangle. By discussing the diorism in Elements, ancient Greek mathematician proved the existence of defined object by postulates or theorems. Therefore, the existence of mathematical object is verifiability in the axiom system. From this perspective, construction is the main method to guarantee the existence in the Elements. Furthermore, we suggest some implications about the existence of mathematical objects in school mathematics.