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The null sign (∅) is often used in mathematics for denoting the empty set. The same letter in linguistics represents zero , the lack of an element. It is commonly used in phonology , morphology , and syntax .
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 ...
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 set theory, the empty set, that is, the set with zero elements, denoted "{}" or "∅", may also be called null set. [3] [5] In measure theory, a null set is a (possibly nonempty) set with zero measure. A null space of a mapping is the part of the domain that is mapped into the null element of the image (the inverse image of the null element).
Equivalently, a convex set or a convex region is a set that intersects every line in a line segment, single point, or the empty set. [1] [2] For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set in the plane is always a convex curve.
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
Book 3 of Euclid's Elements deals with the properties of circles. Euclid's definition of a circle is: A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.
Circles on the sphere are, like circles in the plane, made up of all points a certain distance from a fixed point on the sphere. The intersection of a sphere and a plane is a circle, a point, or empty. [18] Great circles are the intersection of the sphere with a plane passing through the center of a sphere: others are called small circles.
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