Number Classification

Chairs and Plants

The number of chairs in a classroom is usually between 0 and 30. Let c represent the number of chairs in a classroom, then we can say

    \[0\le c \le 30\]

Let’s be more precise. Unless there has been some kind of unusual interaction with the chairs, there are probably not say 10.25 chairs, even though 10.25 satisfies the inequality. We mean between 0 and 30, whole numbers only. Therefore

    \[0 \le c \le 30, \text{where } c \in \mathbb{Z}\]

The letter-like-symbol \mathbb{Z} is used for integers, that is, whole numbers.

On the other hand, if I am measuring an amaryllis plant that will grow to 60 cm, I can say that during its growth period it is is between zero and 60 cm.

In this case, it can be 10.25 cm. It will grow through all possible values. Let h represent the height of an amaryllis plant in cm, and we can say

    \[0 \le h \le 60, \text{where }h \in \mathbb{R}\]

The letter-like-symbol \mathbb{R} is used for real numbers, that is, all numbers represented on a continuous number line from negative infinity to positive infinity.

The Default

If you do not mention a particular set of numbers, we assume the set of real numbers.

The four major number sets

In this course, you are expected to be familiar with Natural Numbers, Integers, Rational Numbers and Real Numbers. Click the image or the link to the mathisfun page to see them described more fully.