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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.
In mathematics, the triple bar is sometimes used as a symbol of identity or an equivalence relation (although not the only one; other common choices include ~ and ≈). [7] [8] Particularly, in geometry, it may be used either to show that two figures are congruent or that they are identical. [9]
An equality symbol (sometimes, identity symbol) = (see § Equality and its axioms below). Not all of these symbols are required in first-order logic. Either one of the quantifiers along with negation, conjunction (or disjunction), variables, brackets, and equality suffices. Other logical symbols include the following:
In fact, every element can be a left identity. In a similar manner, there can be several right identities. But if there is both a right identity and a left identity, then they must be equal, resulting in a single two-sided identity. To see this, note that if l is a left identity and r is a right identity, then l = l ∗ r = r.
A ground term is a term that contains no variables. Ground terms may be defined by logical recursion (formula-recursion): Elements of are ground terms;; If is an -ary function symbol and ,, …, are ground terms, then (,, …,) is a ground term.
A left identity element that is also a right identity element if called an identity element. The empty set ∅ {\displaystyle \varnothing } is an identity element of binary union ∪ {\displaystyle \cup } and symmetric difference , {\displaystyle \triangle ,} and it is also a right identity element of set subtraction ∖ : {\displaystyle ...
The reason for this is that zero is the identity element for addition. Similarly, the product of the elements of the empty set (the empty product) should be considered to be one, since one is the identity element for multiplication. [6] A derangement is a permutation of a set without fixed points.
In a figure / ground ambigram, letters fit together so the negative space around and between one word spells another word. [42] In Gestalt psychology, figure–ground perception is known as identifying a figure from the background. For example, black words on a printed paper are seen as the "figure", and the white sheet as the "background".