**Natural Numbers**– The set of counting numbers { 1, 2, 3, 4, 5, …}.

**Whole Numbers**– Natural numbers combined with zero { 0, 1, 2, 3, 4, 5, …}.

**Integers**– Positive and negative whole numbers including zero {…,−5, −4, −3,−2, −1, 0, 1, 2, 3, 4, 5…}.

**Rational Numbers**– Any number of the form

*a*/

*b*where

*a*and

*b*are integers where

*b*is not equal to zero.

**Irrational Numbers**– Numbers that cannot be written as a ratio of two integers.

When comparing real numbers, the larger number will always lie to the right of smaller numbers on a number line. It is clear that 15 is greater than 5, but it might not be so clear to see that −5 is greater than −15.

Use

**inequalities**to express order relationships between numbers.< "less than"> "greater than"≤ "less than or equal to"≥ "greater than or equal to"

It is easy to confuse the inequalities with larger negative values. For example,

−120 < −10 “

*Negative 120 is less than negative 10.*”
Since −120 lies further left on the number line, that number is less than −10. Similarly, zero is greater than any negative number because it lies further right on the number line.

0 > −59 "

*Zero is greater than negative 59.*"**Write the appropriate symbol, either < or >.**

**List three integers satisfying the given statement**. (Answers may vary.)

**Absolute Value**– The distance between 0 and the real number

*a*on the number line, denoted |

*a*|. Because the absolute value is defined to be a distance, it will always be positive. It is worth noting that |0| = 0.

**Point of confusion**: You may encounter negative absolute values like this −|3|. Notice that the negative is in front of the absolute value. Work the absolute value first, then consider the opposite of the result. For example,

−|3| = −3

−|−7| = −7

Believe it or not, the above are correct! Look out for this type of question on an exam.

**Video Examples on YouTube:**