Algebra 2 Vocab That I Need To Know

transitivity for equality

if the first item is equal to the second, and the second item is equal to the third, then the first item is also equal to the third. Symbolically, if a = b and b = c, then a = c.

transitivity for order

a fundamental mathematical property stating that if an element A is in a specific order relation to B, and B is in the same relation to C, then A is also in that relation to C. For example, if A < B and B < C, then A < C, demonstrating a logical chain where indirect relationships lead to a direct conclusion

symmetry for equality

if one quantity is equal to another, then the second quantity is equal to the first

reflexive axiom for equality

any value or object is equal to itself, represented mathematically as a = a.

trichotomy

In algebra, the trichotomy law (or property) states that for any two real numbers, exactly one of the following three possibilities must be true:

a is less than b

𝑎<𝑏

(a is less than b),

a equals b

𝑎=𝑏

(a equals b), or

a is greater than b

𝑎>𝑏

(a is greater than b).