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  2. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T. We can see also that, with the same premise, another conclusions are valid: columns 12, 14 and 15 are T.

  3. Mathematical universe hypothesis - Wikipedia

    en.wikipedia.org/wiki/Mathematical_universe...

    The idea that math is 'out there' is incompatible with the idea that it consists of formal systems." Tegmark's response [10]: sec VI.A.1 is to offer a new hypothesis "that only Gödel-complete (fully decidable) mathematical structures have physical existence. This drastically shrinks the Level IV multiverse, essentially placing an upper limit ...

  4. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems ; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms ...

  5. List of axioms - Wikipedia

    en.wikipedia.org/wiki/List_of_axioms

    Together with the axiom of choice (see below), these are the de facto standard axioms for contemporary mathematics or set theory.They can be easily adapted to analogous theories, such as mereology.

  6. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Some students studying math may develop an apprehension or fear about their performance in the subject. This is known as math anxiety or math phobia, and is considered the most prominent of the disorders impacting academic performance. Math anxiety can develop due to various factors such as parental and teacher attitudes, social stereotypes ...

  7. Deduction theorem - Wikipedia

    en.wikipedia.org/wiki/Deduction_theorem

    In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly axiomatize that hypothesis, i.e. to prove an implication A → B, it is sufficient to assume A as a hypothesis and then proceed to derive B.

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