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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.
Here is an example of an argument that fits the form conjunction introduction: Bob likes apples. Bob likes oranges. Therefore, Bob likes apples and Bob likes oranges. Conjunction elimination is another classically valid, simple argument form. Intuitively, it permits the inference from any conjunction of either element of that conjunction.
If is used as notation to designate the result of replacing every instance of conjunction with disjunction, and every instance of disjunction with conjunction (e.g. with , or vice-versa), in a given formula , and if ¯ is used as notation for replacing every sentence-letter in with its negation (e.g., with ), and if the symbol is used for ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
A method of encoding mathematical and logical symbols and expressions as natural numbers, introduced by Kurt Gödel as part of his incompleteness theorems. Gödel sentence A self-referential sentence constructed in formal systems to demonstrate Gödel's incompleteness theorems, asserting its own unprovability within the system. Gödel-Dummett logic
Wedge (∧) is a symbol that looks similar to an in-line caret (^). It is used to represent various operations. In Unicode, the symbol is encoded U+2227 ∧ LOGICAL AND (∧, ∧) and by \wedge and \land in TeX. The opposite symbol (∨) is called a vel, or sometimes a (descending) wedge.
Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction) [1] [2] [3] is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof .
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 ...