sum,
n. 1a. the result of the addition of numbers, quantities, etc.
b. formally, the number derived from a pair of given numbers such that if the latter are the numbers of elements in two disjoint sets, the former is the total number of elements in either set.
2. the limit of the sequence of partial sums of the firstn terms of an infinite series, asn tends to infinity. For example, the series
+... has sum 2, since that is the limit of the sequence of partial sums
1,11/2, 13/4, 17/8,....
This is in general the most convenient choice for the sum of a series, but others are possible; see Cesaro summation. See also sigma, rearrangement. 3. (informal) any arithmetical problem or calculation. 4. logical sum. another name for disjunction or union. 5. set-theoretic sum. another name for union. Compare disjoint union.
b. formally, the number derived from a pair of given numbers such that if the latter are the numbers of elements in two disjoint sets, the former is the total number of elements in either set.
2. the limit of the sequence of partial sums of the firstn terms of an infinite series, asn tends to infinity. For example, the series
+...1,11/2, 13/4, 17/8,....
This is in general the most convenient choice for the sum of a series, but others are possible; see Cesaro summation. See also sigma, rearrangement. 3. (informal) any arithmetical problem or calculation. 4. logical sum. another name for disjunction or union. 5. set-theoretic sum. another name for union. Compare disjoint union.