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Shall and will. Shall. and. will. Shall and will are two of the English modal verbs. They have various uses, including the expression of propositions about the future, in what is usually referred to as the future tense of English. Historically, prescriptive grammar stated that, when expressing pure futurity (without any additional meaning such ...
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [9] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such ...
projection. A projection is, roughly, a map from some space or object to another that omits some information on the object or space. For example, R 2 → R , ( x , y ) ↦ x {\displaystyle \mathbb {R} ^ {2}\to \mathbb {R} , (x,y)\mapsto x} is a projection and its restriction to a graph of a function, say, is also a projection.
A modal verb is a type of verb that contextually indicates a modality such as a likelihood, ability, permission, request, capacity, suggestion, order, obligation, necessity, possibility or advice. Modal verbs generally accompany the base (infinitive) form of another verb having semantic content. [1] In English, the modal verbs commonly used are ...
Information theory. Information theory is the mathematical study of the quantification, storage, and communication of information. The field was established and put on a firm footing by Claude Shannon in the 1940s, [1] though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley.
The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been found in documents dated as far back as 1631. [1] In mathematical writing, the greater-than sign is typically placed between two values being ...
The Latin maxim ignoramus et ignorabimus, meaning "we do not know and will not know", represents the idea that scientific knowledge is limited. It was popularized by Emil du Bois-Reymond, a German physiologist, in his 1872 address "Über die Grenzen des Naturerkennens" ("The Limits of Science"). [1]