integral与integer的用法辨析及翻译建议:
1. 词源与核心语义:
- integer源自拉丁语"integrum"(完整之物),数学中专指"整数"(如±1,±2等)
- integral源自同一词根,但强调"构成整体必需的部分"
2. 典型用法对比:
数学领域:
- integer:严格表示不含分数/小数的数字(译作"整数")
例:The set of integers includes negative numbers.(整数集合包含负数)
- integral:多指"积分"(微积分概念)或"构成整体必需的"
例:Integral calculus is funda ...(以上内容有节略,please sign in for more)
Constituting a whole together with other parts or factors; not omittable or removable
Of, pertaining to, or being an integer.
Relating to integration.
Whole; undamaged.
A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.
Antiderivative
A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
necessary to make a whole complete; essential or fundamental
included as part of a whole rather than supplied separately
having all the parts that are necessary to be complete
of or denoted by an integer.
involving only integers, especially as coefficients of a function.
a function of which a given function is the derivative, i.e. which yields that function when differentiated, and which may express the area under the curve of a graph of the function.
a function satisfying a given differential equation.
Constituting a whole together with other parts or factors; not omittable or removable
Of, pertaining to, or being an integer.
Relating to integration.
Whole; undamaged.
A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.
Antiderivative
A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
necessary to make a whole complete; essential or fundamental
included as part of a whole rather than supplied separately
having all the parts that are necessary to be complete
of or denoted by an integer.
involving only integers, especially as coefficients of a function.
a function of which a given function is the derivative, i.e. which yields that function when differentiated, and which may express the area under the curve of a graph of the function.
a function satisfying a given differential equation.