CLAA Arithmetic 20

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How do we denominate Integers?

The general way to denominate Integers proceeds by Tens, using the ten figures or digits 1,2,3,4,5,6,7,8,9 and 0. The First Denomination is that of Unites, the Second Denomination is that of Tens, the Third Denomination is that of Hundreds, and so on.

What does the digit or character "0" represent?

The character "0" represents nothing in itself, but it is used as a place holder to distinguish a Denomination from another. It is also called a Cypher.

What are Periods?

For numbers with more than three digits, we divide them into Periods, with each Period being a group of three digits, starting from the units place. The first Period is called the Period of Units, the second Period is called the Period of Thousands, the third Period is called the Period of Millions, and so on.

What is a Decimal Fraction?

A Decimal Fraction is a proper fraction written in decimal form. I.e., written as a "0" followed by a point "." and then a number.

How do we denominate Decimal Fractions?

We divide Decimal Fractions into Denominations of Tenths, Hundredths, Thousandths, and so on.

How many types of Decimal Fractions are there?

There are two types of Decimal Fractions: Exact decimal fractions and Approximant decimal fractions. An Exact decimal fraction is one which expresses the Ratio of the Part to the Whole exactly, like 0.4, which is 4/10 or 3/5. An Approximant decimal fraction is one which does not express it exactly but approaches infinitely near it, like 0.33333333, with infinitely many 3's, which is 1/3.

How are numbers divided?

Numbers, both integers and mixed numbers, are divided into Monomes and Polynomes.

What is a Monome?

A Monome is a number which consists of only one significant digit into one Denomination, with all other digits a Cypher. In other words, all digits are "0" except for one of them.

What is a Polynome?

A Polynome is a number with more than one significant digit.

What relationships exist between Monomes?

Monomes are either Homogeneous or Heterogeneous.

What are Homogeneous and Heterogeneous Monomes?

Homogeneous Monomes are Monomes of the same Denomination. Heterogeneous Monomes are Monomes of different Denominations.

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