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2. Language of mathematics - Wikipedia

   en.wikipedia.org/wiki/Language_of_mathematics

   The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.

3. Sentence (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Sentence_(mathematical_logic)

   A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values: as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.

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5. First-order logic - Wikipedia

   en.wikipedia.org/wiki/First-order_logic

   In this example, both sentences happen to have the common form () for some individual , in the first sentence the value of the variable x is "Socrates", and in the second sentence it is "Plato". Due to the ability to speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic.

6. Critical mathematics pedagogy - Wikipedia

   en.wikipedia.org/wiki/Critical_mathematics_pedagogy

   Those who build their critical mathematics pedagogy out of critical pedagogy focus on empowerment of the learners as experts and actors for change in their own world. . Critical mathematics pedagogy demands that students and teachers use mathematics to understand "relations of power, resource inequalities between different social groups and explicit discrimination" [1] in order to take action for

7. Mathematical logic - Wikipedia

   en.wikipedia.org/wiki/Mathematical_logic

   The Löwenheim–Skolem theorem (1919) showed that if a set of sentences in a countable first-order language has an infinite model then it has at least one model of each infinite cardinality. This shows that it is impossible for a set of first-order axioms to characterize the natural numbers, the real numbers, or any other infinite structure up ...