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incomplet1906
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If t is the term x*y*z of the language for group theory, why is x*y not a subterm of t? isn't (x*y)*z = x*(y*z) = x*y*z, meaning that x*y is a subterm by definition?
It is not necessary that every combination of variables and operators will result in a valid subterm in the context of group theory. In this case, x*y may not be a subterm of t due to the specific rules and definitions of the language.
Yes, x*y may be a valid subterm in other contexts or languages that have different rules and definitions for subterms. It is important to understand the specific context in which the term is being evaluated.
The rules and definitions of group theory are based on mathematical concepts and principles, which may not necessarily align with our intuition or common sense. Therefore, the reason for x*y not being a subterm may be based on these underlying principles.
In group theory, a term is considered a valid subterm if it follows the specified rules and definitions of the language. These rules may vary depending on the specific context or application of group theory.
The concept of subterms is closely related to other concepts in group theory, such as subgroups and cosets. These concepts all involve breaking down a larger structure into smaller, more manageable parts, and understanding how these parts interact with each other.