1.The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356…, the square root of 2, an irrational algebraic number). Included within the irrationals are the transcendentalnumbers, such as π (3.14159265…).

The Real Numbers did not have a name before Imaginary Numbers were thought of. They got called "Real" because they were not Imaginary. That is the actual answer!

We can use the number line to help us add. We always move to the right to add.

We can use the number line to help us subtract. We always move to the left to subtract.

4.Numbers on the left are smaller than numbers on the right.

Examples:5 is smaller than 8−1 is smaller than 1−8 is smaller than −5

Numbers on the right are larger than numbers on the left.

Examples:8 is larger than 51 is larger than −1−5 is larger than −8

Try this interactive number line (click to mark):

5.A number with no fractional part. 

• the counting numbers {1, 2, 3, ...}, 
• zero {0}, 
• and the negative of the counting numbers {-1, -2, -3, ...}

We can write them all down like this: {..., -3, -2, -1, 0, 1, 2, 3, ...}

Examples of integers: -16, -3, 0, 1, 198