Definition:Zero Element/Also defined as

Zero Element: Also defined as

Beware of the usage of the term zero element to mean the identity element under the operation of addition:

$a + 0 = a = 0 + a$

While zero is indeed a zero element under the operation of multiplication:

$a \times 0 = 0 = 0 \times a$

it is not, strictly speaking, a zero element of addition.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): zero element
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): zero element