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Contrast the term primitive notion, which is a core concept not defined in terms of other concepts. Primitive notions are used as building blocks to define other concepts. Contrast also the term undefined behavior in computer science, in which the term indicates that a function may produce or return any result, which may or may not be correct.
Alfred Tarski explained the role of primitive notions as follows: [4]. When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions of this discipline that seem to us to be immediately understandable; the expressions in this group we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings.
A student at Level 0 or 1 will not have the same understanding of this term. The student does not understand the teacher, and the teacher does not understand how the student is reasoning, frequently concluding that the student's answers are simply "wrong". The van Hieles believed this property was one of the main reasons for failure in geometry.
In Euclidean geometry, similarity is used to describe objects that have the same shape, while congruence is used to describe objects that are the same in both size and shape. [69] Hilbert, in his work on creating a more rigorous foundation for geometry, treated congruence as an undefined term whose properties are defined by axioms.
In other words, the elements of geometry form a system which is not susceptible of extension, if we regard the five groups of axioms as valid. The old axiom V.2 is now Theorem 32. The last two modifications are due to P. Bernays. Other changes of note are: The term straight line used by Townsend has been replaced by line throughout.
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