**Glossary of terms used in counting systems**

We will revise the English vocabulary we have used in the series of four articles to clarify the semantics of this topic. Counting systems are deeply integrated into every language. A **counting system** is composed of all these words:

**System:** A set of ideas working together to achieve a purpose. It can require you to use instruments and tools. Example: *A writing system is composed of characters, words and a grammar structure, this helps us communicate via the sense of sight (reading). A stone, piece of paper or a computer display is the appropriate tool for this.*

**Symbol:** Any figure or shape written on paper for reading to denote voices (Latin Alphabet and Chinese characters) or numerals (Hindu-Arabic number symbols).

**Sequence:** Without a proper sequence of numerals or symbols, size associated with the numbers will be meaningless.

**Numerals:** Refers to words associated with fingers opening. These words can be read aloud and are part of very language. We simply give **names** to fingers open, just as parents give names to their children. Example: one, two, three, four and five.

**Numbers:** Refers to symbols used associated with the numerals. Sometimes used interchangeably with the word “numerals”. Can also be called “**Number Characters**” or “**Digits**“. Example: 1, 2, 3, 4, 5.

**Counting:** Reading aloud the defined and set-up sequence of numbers. We can also subvocalize counting (without reading aloud). Based on that sequence, it is used as an indicator of size/quantity and used for the question: How many?

**Number writing system:** Way of writing numbers for communication. Includes a set of symbols called numbers and system for **indicating** the size of a number. Ancient cultures developed their own number writing systems, but due to the worldwide influence of Western culture, we all now use the **Hindu-Arabic** or **Roman** number writing system.

**Size indication system:** Part of any number writing system of any culture and used along with the symbols called numbers. Place value system or positional notation system is an example of this. Sometimes a number alone will indicate size, if the place value system is not used, as in the Roman and East Asian number writing system.

**Place Value:** The size indication system of the popular Hindu-Arabic number writing system. The position of a number character in a number. Example: *The place value of the number character “5” in the number 1,569 is in the hundreds.*

**Number display system:** Setting the amount of number characters that can be used in each place value or setting the amount of beads in every column of the abacus. For convenient everyday usage, it must match the vocabulary used in everyday language. Example: The decimal English, French and Japanese vocabulary for numerals matches the decimal display system.

**Why is the predefined sequence is important?**

Scientists sometimes use their knowledge of logarithms to explain the empirical data they found out from their observations.

We have to learn basic mathematics before we can learn logarithms in high school. You have to learn indices before logarithms. You have to learn multiplication before you learn indices.

Since they have to learn mathematics, they have to learn counting first, otherwise they cannot even add, subtract, multiply and divide.

To be able to **count properly**, we have to learn the sequence of numbers in the order taught by the teacher just like we learn ABC (Latin Alphabet). We were taught the Hindu-Arabic base-10 counting system. The correct sequence is 1,2,3,4,5… not 4,1,5,3,2…

The US English keyboard has the wrong sequence of letters, with respect to the alphabet song they taught you in kindergarten. it is A,B,C,D,E… , not Q,W,E,R,T…. You won’t know the phrase “alphabetical order” without learning the alphabet song. The alphabet song made it easy for children to remember the correct sequence, then we grow up with it.

**What do we need for the most reliable counting system in everyday life?**

It must have a properly defined sequence of numerals. The sequence of numerals need to be defined like the sequence of sounds in a song. This sequence gives a continuum pattern of numbers and numerals. These conditions are the requirement of **counting**.

Preparing a cup of tea or watering the plants in the backyard has a sequence.

The number writing system must have an convenient way of writing the number symbols and a convenient way of indicating size. The symbols must be easy to write. This is the place value system which is more consistent in showing the size based on the number character used. The **Hindu-Arabic** number writing system is the best for this.

We need a numeral vocabulary that is appropriate to the number display system. We have a decimal vocabulary, so we use the decimal display system in everyday life. The best system for this is the **Decimal** display system, which is the original display system of the Hindu-Arabic number writing system.

Now that we have selected the most reliable counting system, the next topics will talk about how useful counting systems are in comparing.