Answer:
None of the choices
Irrational, Real, Complex
Step-by-step explanation:
Number system:
(since I'm having image upload trouble I'll just do an outline format)
Complex numbers (all numbers we have)
I. Imaginary
- cannot be plotted on number line
-include <em>i</em>, sqrt of (-) #s, variables, |-#s|, etc.
(This includes pure imaginary and imaginary #s: In terms of <em>i</em>, pure imaginary is only b*i, and imaginary is a+b<em>i</em>, a and b being integers)
II. Real numbers: can be plotted on # line (have a real value)
A. Irrational numbers
- Non-repeating, non-terminating (ending) decimals
E.X. : 1.12343123510971324...
- Cannot be expressed as a fraction of 2 integers
- Has a real value (pi, phi, tau, square roots of non-perfect non-negative squares e.x. \sqrt2)
B. Rational
- Can be expressed as fraction of 2 integers
E.x. 0.3333... = 1/3
- Can be expressed as terminating or repeating decimal
E.x. 0.3232... , 0.32, etc.
1. Includes: Fractions and terminating/repeating decimals
2. Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
a. Whole numbers: 0, 1, 2, 3, ...
i. Counting/natural numbers: 1, 2, 3, ...
