The document discusses different methods of counting, including the traditional process of incrementing a counter for each element in a set. It provides examples of counting money, verbal counting, tally marks, and finger counting. Additionally, it covers counting infinite and finite sets in mathematics, the history of counting originating in Sumeria, and the fundamental counting principle for determining outcomes in probability problems. The document is about the various ways and concepts related to counting in mathematics.

1. Counting Method
Jori Dixon
4/22/19
Math 118
Professor Lewis

2. Process of Counting
• The process of counting determines the number of elements of a finite set of objects. The
traditional way of counting consists of continually increasing a (mental or spoken) counter
by a unit for every element of the set, in some order, while marking (or displacing) those
elements to avoid visiting the same element more than once until no unmarked elements
are left, if the counter was set to one after the first object, the value after visiting the final
object gives the desired number of elements.

3. Example 1: Counting Money
• Counting sometimes involves numbers other than
one; for example, when counting money, counting
out change, "counting by twos" (2, 4, 6, 8, 10,
12, ...), or "counting by fives" (5, 10, 15, 20, 25, ...).

4. Forms of Counting
• Verbal
• Tally Marks
• Finger Counting

5. Example 2: Verbal
Counting

6. Counting Tally Marks

7. Finger Counting

8. Counting in Mathematics
• Infinite Sets
• Finite Sets
• Real Numbers

9. Example 3: Counting
Infinite and Finite Sets

10. History of Counting
• Numbers, and counting, began about 4,000 BC in Sumeria, one of the earliest
civilizations. ... This was a big step in the history of numbers and counting because with
that step subtraction, and thus the invention of arithmetic, was invented. In the beginning
Sumerians kept a group of clay cones inside of clay pouches.

11. Elementary Arithmetic
• Addition
• Subtraction
• Division
• Multiplication

12. Example 4: Elementary
Arithmetic

13. Fundamental Counting Principle
• A way to figure out the number of outcomes in a probability problem.
Basically, you multiply the events together to get the total number of
outcomes.

14. Example 5: Fundamental Counting Principle

15. Board Games
• Snakes and Ladders
• Monopoly
• Sorry!