Definition
Real number
Real numbers are all values that have positions along the continuous number line.
Continue from this idea into connected AXIO math.
Boundary check: Negative numbers and irrational numbers are real too.
What it means
Whole numbers, negative numbers, fractions, terminating or repeating decimals, and numbers such as √2 all live on one continuous number line. “Real” names this whole collection, not only numbers used in everyday measurements.
Remember it
One continuous number line, every point: all of those values are real numbers.
Example
−3, 1/4, 0.7, and √2 are all real numbers because each one has a location on the number line.
Watch for
Real does not mean positive or easy to write: negative numbers and irrational numbers are real.
Common mix-up
Numbers involving √−1 are not points on the real number line and are outside this real-number set.
Exact meaning
Every real number corresponds to one location on a continuous number line, and every location on that line corresponds to a real number. This set contains both rational and irrational numbers.