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Let $a + b$ denote the operation of addition on two objects $a$ and $b$.

Then the result $a + b$ is referred to as the sum of $a$ and $b$.

Note that the nature of $a$ and $b$ has deliberately been left unspecified.

They could be, for example, numbers, matrices or more complex expressions constructed from such elements.

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.