Algebra - vocabulary

Noun   
Suffix: -ity

Pronunciation
/ˌkɒmjuːtə'tɪvɪti/ listen

Meaning
The commutativity is a property of a binary operation. If the property holds, the change of the order of the operands does not change the result.

Example
For addition:               a + b = b + a
For multiplication:      ab = ba

Synonym
Commutative property

Antonym
Noncommutativity

Similar words
To commute      verb          /kɒ'mjuːt/           listen
Commutable     adjective   /kəˈmjuːtəb(ə)l/  listen
Commutative    adjective   /kɒˈmjuːtətɪv/     listen
Commuted       adjective   /kɒ'mjuːtɪd/        listen

Etymology
From medieval Latin commūtātīvus (French (14th cent.) commutatif , -ive ), < Latin commūtāt- participial stem of commūtāre to

Source
OED

 /kənˈstrʌk.ʃən/

A finite sequence of steps. The steps are defined by author of the task, classical example is Eucleidian construction by straightedge and compass.

Adjective
Prefix: co-

Pronunciation
/ˈkoʊˌpraɪm/ listen

Meaning
Coprime integers are two or more numbers that have no common factor except unity. In other words, there is no whole number that divides them both without any remainder. This is equivalent to their greatest common divisor being 1.

Examples
The numerator and denominator of a reduced fraction are coprime, for instance, 7/8.
Integers 15 and 8 are coprime. Integers 8 and 6 are not coprime.

Note

• A set of integers can also be called coprime if its elements share no common positive factor except 1.
• A stronger condition on a set of integers is pairwise coprime. It means that numbers n₁ and n₂ are coprime for every pair (n₁, n₂) of different integers in the set. The set {2, 5, 8} is coprime but it is not pairwise coprime since 2 and 8 are not coprime.

Synonyms
Relatively prime, mutually prime

Antonym
Not coprime

Etymology
Derived from prime, that is partly from French, partly from Latin (French prime; Latin prīmus)
The prefix co- is from Latin. It means together, mutually, jointly, etc.

Source
OED