Definition:Sum

Disambiguation

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Sum may refer to:

• Arithmetic:
  • Under the operation of addition of two numbers $a$ and $b$, the sum is the result of the operation $a + b$.

• Algebra:
  • A summation is a repeated addition on a sequence (either finite or infinite) of numbers, usually signalled by the summation sign: $\ds \sum$

• Abstract Algebra, Group Theory:
  • Definition:Direct Sum

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Also see

• Definition:Product
• Definition:Difference

Linguistic Note

In natural language, the word sum is often used to mean the process of operation of any arithmetical calculation.

This probably originates from elementary school, where the first excursions into arithmetic occurs via (natural number) addition.

Consequently, at that level, all such arithmetic lessons are often referred to as sums.

To those with mathematical anxiety, the very word sums may be distressing, while in the humour of children's comics, a popular punishment for a child would be to be sat down at a desk in front of a book titled hard sums.