Definition:Additive Inverse/Also defined as

Additive Inverse: Also defined as

Some sources make special issue of the nature of a group when its underlying set is a subset of, or derived directly from, numbers themselves.

In such treatments, the inverses of a group whose operation is addition are then referred to as additive inverses.

On $\mathsf{Pr} \infty \mathsf{fWiki}$ we consider all groups, whatever their nature, to be instances of the same abstract concept, and therefore make no such distinction.

Some sources confuse and muddy the water still further by calling an additive inverse an inverse in any group whose notation is such that it uses $+$ as the symbol to denote the group operation and use $0$ to denote the identity.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): additive inverse
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): additive inverse
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): additive inverse