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In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore. While it is not generally used in formal writing, it is used in mathematics and shorthand.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice.
where is a metalogical symbol meaning that is a syntactic consequence of and in some logical system; or as the statement of a functional tautology or theorem of propositional logic: ( ( P → Q ) ∧ ¬ Q ) → ¬ P {\displaystyle ((P\to Q)\land \neg Q)\to \neg P}
In general, an expression denotes or names a mathematical object, and plays therefore in the language of mathematics the role of a noun phrase in the natural language. An expression contains often some operators , and may therefore be evaluated by the action of the operators in it.
Paul Halmos claims to have pioneered the use of a solid black square (or rectangle) at the end of a proof as a Q.E.D. symbol, [16] a practice which has become standard, although not universal. Halmos noted that he adopted this use of a symbol from magazine typography customs in which simple geometric shapes had been used to indicate the end of ...
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...