Definition of Order on a number line:

If a and b are real numbers, a is less than b if b – a is positive.

a < b

Inequality Symbols:

< is less than

> is greater than

< is less than or equal to

\geq is greater than or equal to

Subsets of real numbers are called intervals.

a, b are the endpoints

Bounded Intervals have 2 endpoints.

[a,b]      Closed        a\leq x\leq b

(a,b)     Open          a< x< b

[a,b)                        a\leq x< b

(a,b]                        a< x\leq b

More Symbols:    \infty    positive infinity     and         -\infty          negative infinity

Unbounded Intervals have one or both endpoints that are \infty and/or -\infty.

[a,\infty)                           x\geq a

(a,\infty)        Open        x> a

(-\infty,b]                       x\leq b

(-\infty,b)      Open       x< b

(-\infty, \infty)      The Entire real number line         -\infty < x< \infty

Law of Trichotomy

For any two real numbers a and b, precisely one of three relationships is possible:

a= b       or         a< b         or        b< a

 

 

Filed under: Pre-requisites for Pre-Calculus

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