Translation guide
In mathematics, an identity element is a special element in a set that leaves other elements unchanged when combined with them. This guide covers how to express this concept in Japanese.
The element in a set that, when combined with any other element via a binary operation, leaves that element unchanged.
Standard term for identity element in abstract algebra. Used for groups, rings, etc.
The identity element of a group is uniquely determined.
Less common synonym for identity element, sometimes used in older texts.
The identity element for this operation is 0.
Phrase meaning 'is the identity element'. Used in definitions.
e is the identity element of this group.
Specifically the additive identity (0 in many structures).
Specifically the multiplicative identity (1 in many structures).
In mathematics, always use 単位元 for the general concept. For specific operations, you can say 加法単位元 (additive identity) or 乗法単位元 (multiplicative identity).
The additive identity in real numbers is 0.
The multiplicative identity is often 1.