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Additive notation uses $+$ for the group operation and $0$ for the identity element, while multiplicative notation uses $\times$ for the operation and $1$ for the identity. These are notational conventions for abstract groups and do not require the elements to be numbers.

Conditions: Used for abstract groups.; The choice of notation changes the symbols for operation and identity but not the underlying group structure.

Additive notation uses $+$ for the group operation and $0$ for the identity element, while multiplicative notation uses $\times$ for the operation and $1$ for the identity. These are notational conventions for abstract groups and do not require the elements to be numbers.

Conditions: Used for abstract groups.; The choice of notation changes the symbols for operation and identity but not the underlying group structure.