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The nabla is a triangular symbol resembling an inverted Greek delta: [1] or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic Greek word νάβλα for a Phoenician harp, [2] [3] and was suggested by the encyclopedist William Robertson Smith in an 1870 letter to Peter Guthrie Tait.
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 ...
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.
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.
In classical mathematics, every injective function f with a nonempty domain necessarily has a left inverse; however, this may fail in constructive mathematics. For instance, a left inverse of the inclusion {0,1} → R of the two-element set in the reals violates indecomposability by giving a retraction of the real line to the set {0,1}. [22]
It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero ( ) sets and it is by definition equal to the empty set. For explanation of the symbols used in this article, refer to the table of mathematical symbols.
In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad impossibile. [3] A mathematical proof employing proof by contradiction usually proceeds as follows: The proposition to be proved is P. We assume P to be false, i.e., we assume ¬P. It is then shown that ¬P implies ...
In elementary mathematics, the additive inverse is often referred to as the opposite number, [3] [4] or its negative. [5] The unary operation of arithmetic negation [6] is closely related to subtraction [7] and is important in solving algebraic equations. [8] Not all sets where addition is defined have an additive inverse, such as the natural ...