# Why is there no (definite) article before "unity" in the mathematical sense?

Example:

x is equal to unity

("unity" has to do with a "unit", i.e. 1, not "the state of being joined together or in agreement".)

• Actually, no not obviously since there is such little context in your post. Second, that's actually not true. I'm assuming that you are talking about (abstract/modern) algebra. Then unity is not the same as a unit.
– Em.
Commented Aug 9, 2016 at 20:41
• Very loosely speaking, yes. Here is one definition with which I am familiar: A ring with a multiplicative identity element is a ring with unity; the multiplicative identity element 1 is called "unity." There might be (probably are) other definitions of unit and unity with which I am unfamiliar. Unity is a unit, but not all units are unity (ie 1).
– Em.
Commented Aug 9, 2016 at 20:57
• This mathematical glossary uses the indefinite article with unity, in each of the 13 times unity is used on that page.
– J.R.
Commented Aug 9, 2016 at 21:16
• Well, being content with a simpler definition doesn't mean you'll be answering the question. The framing and the assumptions need to all match. Anyway, for more context, 1 is just a label, not necessarily the number one. For example, 0 (zero) is the multiplicative inverse in the zero ring. So in the zero ring, zero the unity and so you can say zero is 1, or that 1=0 (mind blown, haha). That is why sometimes, we specify that the 1 not equal 0.
– Em.
Commented Aug 9, 2016 at 21:24
• It seems to me we could refer to "a unity" when discussing the mathematical conception, and "the unity" when referring to an instance, or just "unity" when presented as a statement in maths, as it is here! Commented Aug 9, 2016 at 22:42

You are using

unit
unity

...in their sense as mathematical jargon to mean 1.0. They are synonymous.

"Unit" or "unity" are used in this way when values are scaled so that their sum equals 1.0.

unit length
unit vector

Doing so makes "general" calculations easier.

One would not say

equal to the unit
equal to the 1.0

since "unit" is representational shorthand for a number.

• -1: If one were a mathematician, one would most definitely say equal to the unit. Mathematicians treat unity as a mass noun and unit as a countable noun, probably because this is the way they're treated in ordinary English. Commented Sep 24, 2016 at 13:06
• I think that mathematicians treat unity as a name. Commented May 3, 2017 at 23:40