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2. Analogy - Wikipedia

   en.wikipedia.org/wiki/Analogy

   In detail, this means that if two mathematical structures are of the same type, an analogy between them can be thought of as a bijection which preserves some or all of the relevant structure. For example, and are isomorphic as vector spaces, but the complex numbers, , have more structure than does: is a field as well as a vector space.

3. Sentence diagram - Wikipedia

   en.wikipedia.org/wiki/Sentence_diagram

   A sentence diagram is a pictorial representation of the grammatical structure of a sentence. The term "sentence diagram" is used more when teaching written language, where sentences are diagrammed. The model shows the relations between words and the nature of sentence structure and can be used as a tool to help recognize which potential ...

4. Kuratowski closure axioms - Wikipedia

   en.wikipedia.org/wiki/Kuratowski_closure_axioms

   For these operators, one can reach conclusions that are completely analogous to what was inferred for Kuratowski closures. For example, all Kuratowski interior operators are isotonic , i.e. they satisfy [K4'] , and because of intensivity [I2] , it is possible to weaken the equality in [I3] to a simple inclusion.

5. Equivalent definitions of mathematical structures - Wikipedia

   en.wikipedia.org/wiki/Equivalent_definitions_of...

   Second, a mathematical structure may have more than one definition (for example, topological space has at least seven definitions; ordered field has at least two definitions). In the former case, equivalence of two definitions means that a mathematical object (for example, geometric body) satisfies one definition if and only if it satisfies the ...

6. Analogical models - Wikipedia

   en.wikipedia.org/wiki/Analogical_models

   Analogical models, also called "analog" or "analogue" models, seek the analogous systems that share properties with the target system as a means of representing the world. It is often practicable to construct source systems that are smaller and/or faster than the target system so that one can deduce a priori knowledge of target system behaviour.

7. Model theory - Wikipedia

   en.wikipedia.org/wiki/Model_theory

   A structure is said to model a set of first-order sentences in the given language if each sentence in is true in with respect to the interpretation of the signature previously specified for . (Again, not to be confused with the formal notion of an " interpretation " of one structure in another) A model of T {\displaystyle T} is a structure that ...