unit vs unity

[Abstract Idea]

In math(s) it is easy to define the words 'unit' and 'unity' to have plain distinct meanings.
For example usually in algebra one defines 'unity' as a multiplicative identity and 'unit' as an element having a multiplicative inverse.

Regarding common everyday English I ask whether these two words 'unit' and 'unity' have different meanings or are used as synonyms? If they are used as synonyms, which one is more used?

PS Feel free to correct any mistakes in this post

[konungursvia]

Unit is used as in the sciences, a degree or amount in measurement.

Unity rarely means "=1" in spoken English, and usually refers to harmony and cooperation between two or more parties.

[Abstract Idea]

Unit is used as in the sciences, a degree or amount in measurement.

Unity rarely means "=1" in spoken English, and usually refers to harmony and cooperation between two or more parties.

Thanks konungursvia. If the word unity rarely means "=1" in spoken English is there another one used instead?

By the way I just remembered another similar word wich also has a precise meaning in math(s): 'unitary' (for example a unitary matrix has unity determinant). So, is the word 'unitary' also used in spoken English?

[PROESL]

Thanks konungursvia. If the word unity rarely means "=1" in spoken English is there another one used instead?

By the way I just remembered another similar word wich also has a precise meaning in math(s): 'unitary' (for example a unitary matrix has unity determinant). So, is the word 'unitary' also used in spoken English?

unitary - This word doesn't sound like ordinary spoken English to me. It sounds like a technical word.