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In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
Let T denote a set of training examples, each of the form (,) = (,,,...,,) where () is the value of the attribute or feature of example and y is the corresponding class label. The information gain for an attribute a is defined in terms of Shannon entropy as follows.
The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers. The Chinese remainder theorem (expressed in terms of congruences) is true over every principal ideal domain.
This is the form of the remainder term mentioned after the actual statement of Taylor's theorem with remainder in the mean value form. The Lagrange form of the remainder is found by choosing () = + and the Cauchy form by choosing () =. Remark.
Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b e mod m. From the definition of division, it follows that 0 ≤ c < m .
This is used to calculate each party's seat entitlement. Every party is assigned the integer portion of this entitlement, and any seats left over are distributed according to a specified rule. By far the most common kind of quota method is the largest remainders method , which assigns any leftover seats over to "plurality" winners (the parties ...
Equivalently, the odd integers (1, 3, 5…) can be used to calculate the averages instead. [ 12 ] [ 20 ] Webster's method produces more proportional apportionments than D'Hondt's by almost every metric of misrepresentation. [ 21 ]
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.