2. The Real Number System

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来自 University of London 的课程

Quantitative Foundations for International Business

164 个评分

University of London

Quantitative Foundations for International Business

164 个评分

课程 3（共 6 门，Specialization International Business Essentials）

This course provides the essential mathematics required to succeed in the finance and economics related modules of the Global MBA, including equations, functions, derivatives, and matrices. You can test your understanding with quizzes and worksheets, while more advanced content will be available if you want to push yourself. This course forms part of a specialisation from the University of London designed to help you develop and build the essential business, academic, and cultural skills necessary to succeed in international business, or in further study. If completed successfully, your certificate from this specialisation can also be used as part of the application process for the University of London Global MBA programme, particularly for early career applicants. If you would like more information about the Global MBA, please visit https://mba.london.ac.uk/. This course is endorsed by CMI

从本节课中

Equations

Although financial models are theoretical frameworks, we often use mathematical tools to work with these models. Mathematical models usually consist of a set of equations, which are designed to describe the structure of the model, and whose solution determines the importance of variables. This week, we will look at equations, including the basic terminology, and the rules for solving equations requiring more than one operation.

Equations- An Introduction3:33

1. Variables, Constants and Parameters6:14

2. The Real Number System6:08

3. Basic Rules7:34

4. Like Terms3:12

5. Translate Phrases into Mathematics6:22

6. Working with Business Formulas5:30

7. Ratio and Proportion6:25

Equations- Summary2:42

与讲师见面

George Kapetanios
Professor of Finance and Econometrics
King's College London

[MUSIC]

The essential elements of every mathematical model are variables and

equations.

It is obvious that each economical variable takes numerical value.

This is why it is important to know the main characteristics of the number system.

Let's start with the real numbers.

Whole numbers such as 1, 2, 3 are called positive integers.

These are the numbers most frequently used in counting y,

the negative counterparts- 1,- 2,- 3,

are called negative integers.

The number 0 is neither positive nor negative.

This is why we can consider it unique.

All the positive and negative integers and

the number zero can be grouped into a single category,

referring to them collectively as the set of all integers.

Along from the integers, the number system

refers to fractions such as 1/3, 1/4, 4/3.

In order to understand the position of a fraction into the number system,

let's think about finding a fraction in a ruler.

The fraction will fill in the gaps between the integers.

Also, there exist negative fractions such

as -3/5 and -5/2, and so forth.

Together, this make up the set of all fractions.

What characterize all fractional numbers is that

each of them can be expressed as the ratio of two integers.

Also, it is important to know that if a number can be expressed

as a ratio of two integers, it's called a rational number.

Notice that since any integer n can be considered as a ratio of n/1,

therefore, also integers are rational.

The set of all integers, in the set of all fractions

together from the set of all irrational numbers.

Moreover, an additional characteristic of

a rational number is that it can be expressed as either

a terminating decimal, like 1/4 equal to 0.25,

or repeating decimal like 1/3 equal to 0.3333,

where some number or series of numbers to the right

of the decimal points is repeated indefinitely.

The opposite of the concept of a rational number is

the one of irrational numbers which are numbers

that can affirm a ratio of two integers numbers.

In particular, an irrational number cannot be

neither terminating decimal, nor a repeating decimal.

For example, the square root of 2 is equal to 1.4142.

We can notice that it is a no repeating and

non-terminating decimal.

The same must be said for the special constant pi which is

equal to 3.1415, which represent the ratio

of the circumference of any circle to its diameter.

And again, is a no repeating,

non-terminating decimal like all irrational numbers.

If we think of an irrational number placed on a ruler,

the number will fill a gap between two rational numbers.

Does the whole ruler represent a continuum which is the set of all real numbers?

That set is indicated with the symbol R.

In the picture that you find in your slides, I listed all the number sets.

If we read from the bottom to the top, this figure

represents a summary of the structure of the real number system.

In our lectures, we use and we are interested only in the real numbers.

However, we should know that they are not the only

numbers that we use in mathematics.

In fact, along with the real number system, we have the imaginary numbers,

which refer to the square roots of negative numbers.

[MUSIC]

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