base,
n. 1a. a side of a polygon, especially a triangle, usually the one at the bottom in a given orientation. For example, DC is the base of the polygon below in the orientation shown,
but any other side may also be referred to as a base.
b. a face of a solid, especially a cone, cylinder, pyramid or prism, usually that on which it stands in a given orientation. For example, EFGH is the base of the cube shown above in the orientation shown, but any other face may also be referred to as a base.
c. any cross section of an infinite cone such that each point in the cone is a unique multiple of a point in the cross section. 2. also called radix. a. the number of distinct single-digit numbers (including zero) in a counting system. For example, the binary system has base 2, as it has only two digits, written 1 and 0, so that the binary numeral 101 represents the decimal number
(1 × 22) + (0 × 21) + (1 × 20) = 5.
The base of a system of notation is thus the number represented by the numeral 10 in that notation. Where it is necessary to be explicit, the base is written subscript after the numeral; so, for example, one writes 1012 = 510. See also place value.
b. the number in terms of which a given number is expressed as a logarithm or exponential. For example, since 1000 = 103, the logarithm of 1000 to base 10 is 3. Where it is necessary to be explicit, the base is written subscript to the symbol; so, for example, one writes log10 1000 = 3.
3. the number of distinct residues in a system of modular arithmetic.
4a. a substructure of a given mathematical structure from which the whole structure can be generated.
b. base for a topology. in particular, a collection of open sets such that every member of the topology is a union of members of the collection.
c. base at a point or local base. more particularly, a subcollection of neighborhoods of the given point with the property that every neighborhood of the point contains a member of the subcollection. This is also called a base for the neighborhood system. See also basis.
b. a face of a solid, especially a cone, cylinder, pyramid or prism, usually that on which it stands in a given orientation. For example, EFGH is the base of the cube shown above in the orientation shown, but any other face may also be referred to as a base.
c. any cross section of an infinite cone such that each point in the cone is a unique multiple of a point in the cross section. 2. also called radix. a. the number of distinct single-digit numbers (including zero) in a counting system. For example, the binary system has base 2, as it has only two digits, written 1 and 0, so that the binary numeral 101 represents the decimal number
(1 × 22) + (0 × 21) + (1 × 20) = 5.
The base of a system of notation is thus the number represented by the numeral 10 in that notation. Where it is necessary to be explicit, the base is written subscript after the numeral; so, for example, one writes 1012 = 510. See also place value.
b. the number in terms of which a given number is expressed as a logarithm or exponential. For example, since 1000 = 103, the logarithm of 1000 to base 10 is 3. Where it is necessary to be explicit, the base is written subscript to the symbol; so, for example, one writes log10 1000 = 3.
3. the number of distinct residues in a system of modular arithmetic.
4a. a substructure of a given mathematical structure from which the whole structure can be generated.
b. base for a topology. in particular, a collection of open sets such that every member of the topology is a union of members of the collection.
c. base at a point or local base. more particularly, a subcollection of neighborhoods of the given point with the property that every neighborhood of the point contains a member of the subcollection. This is also called a base for the neighborhood system. See also basis.