# Why can't we just say 1 instead of "unity"?

I know this is a soft question of sorts but I am curious why we can't just say "1" instead of "unity," e.g. a root of unity.

• ... the concept extends to any algebraic unital ring. Apr 2 '13 at 21:41
• @AsalBeagDubh out of curiosity did you manage to read past the first two paragraphs? "Unfortunately, the term unit is also used to refer to the identity element $1_R$ of the ring, in expressions like ring with a unit or unit ring, and also e.g. 'unit' matrix. (For this reason, some authors call $1_R$ "unity" or "identity", and say that $R$ is a "ring with unity" or a "ring with identity" rather than a "ring with a unit".)" Apr 2 '13 at 21:48
• @oldrinb: Well, I read your second comment as saying that in a unital ring, the word unit only means multiplicative identity. In any case, I think this proves that the term "unity" is confusing!
– user64687
Apr 2 '13 at 21:51
• And, for those folks who are comfortable writing "ring with $1$" for "ring with unit(y)", why not also write "$0$-divisor" vs. "zero-divisor"? Apr 2 '13 at 21:55
• @oldrinb: I get your meaning now! My two cents: I think people prefer "unity" because saying "a ring with one" sounds incomplete: the instinctive response is, "a ring with one what?"
– user64687
Apr 2 '13 at 21:56

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• Never mind I found out. $\$\{\}\{\}\{\}\{\}\{\}\{\}\ Apr 2 '13 at 21:44
• Now, we know ${}{}{}$ Apr 2 '13 at 21:58