# GRE Subject Test: Math : Finite, Infinite, Countable, Not Countable Classifications

## Example Questions

### Example Question #1 : Finite, Infinite, Countable, Not Countable Classifications

Which of the following sets is not an infinite set??

All whole numbers

All numbers  between  and

All whole numbers

Explanation:

Step 1: Determine the difference between Infinite and Finite Sets...

Finite Sets: A set that has very limited elements in it
Infinite Sets: Any set where I can always find another number between two given boundaries.

The Set of integers and rational numbers are infinite sets..
All numbers between  and  is also an infinite set because I can come up with infinite decimal numbers..

The set of whole numbers between  and  inclusive is a finite set because I ask for a specific type of number.. a whole number. Whole numbers cannot be decimals..

### Example Question #2 : Finite, Infinite, Countable, Not Countable Classifications

Which of the following is a finite set?

All real numbers between  and

All whole numbers between  and , inclusive

All whole numbers between  and , inclusive

Explanation:

Note: The set of real numbers , natural numbers  are both infinite sets.
Step 1: The set of real numbers between two numbers  is also an infinite set.

Step 2: The set of whole numbers between  and  inclusive is finite because there are only three numbers that are represented by the set. These numbers are .