Friday, 11 January 2013

NUMBER SYSTEM (2)

by Mr Johari

The world of numbers is certainly mind boggling as demonstrated by the clip 'Donald in Mathmagic Land'
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The diagram above shows different categories of numbers in the number system.
Please find (1) the definition and (2) a few examples of that categories of numbers.
example:
Whole Number : (1) Also called one of the positive integers or zero;
(2) {0, 1, 2, 3,…}.
source: http://dictionary.reference.com/browse/whole+number
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post your responses as a 'comment'

1. Integers are numbers with no fractional part . This includes the counting numbers {1, 2, 3, ...}, zero {0}, and the negative of the counting numbers {-1, -2, -3, ...}
Examples of integers include -16, -3, 0, 1, 198

2. Definition of integer: A whole number; a number that is not a fraction

examples: 1&2

3. Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!

-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10
So, integers can be negative {-1, -2,-3, -4, -5, … }, positive {1, 2, 3, 4, 5, … }, or zero {0}

We can put that all together like this:
Integers = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }

source :http://www.mathsisfun.com/whole-numbers.html

4. 1. An Irrational Number is a real number that cannot be written as a simple fraction. Irrational means not Rational

2. Example: 1.5=3/2(rational) Pi=3.14159...=?/?(irrational)

5. (1): Rational Numbers: They are numbers that can be written as a simple fraction, numbers that is able to end without an eternal set of decimals at the back.
(2)Irrational Numbers: Irratonal Numbers are numbers that are never-ending, and does not have a perfect value.

Examples:
Rational-16.5 (33/2), 3.7 (37/10)
Irrational-Pi(3.141592654...), 1/3 (0.333333...)

6. Whole numbers : (1) Also called counting numbers (2) e.g. 1,2,3,4,5
Integers: (1) An integer is a positive or negative whole number or zero. (2 )e.g -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
Rational Numbers: (1) A number that can be expressed exactly by a ratio of two integers.. (2) e.g. 5, 1.75, 0.001, 1/9
Irrational Numbers: (1) A number that cannot be exactly expressed as a ratio of two integers. (2) e.g. π, √3,
Real Numbers: (1) A rational number or the limit of a sequence of rational numbers. (2) e.g. 1,2,3,4, 3/4, 0.125, 0.333...., 1.1,π, √3,
Imaginary Numbers :(1) An Imaginary Number, when squared, gives a negative result. (2) e.g i, 12.38i, -i, 3i/4, 0.01i, -i/2
Complex Numbers: (1) Complex Number is just two numbers added together (a Real and an Imaginary Number). (2) e.g. 1 + i , 39 + 3i, 0.8 - 2.2i, -2 + πi ,√2 + i/2

7. Rational numbers: (1)A rational number is a number that can be written as a simple fraction (i.e. as a ratio). (2)Example 1.5 is a rational number because 1.5 = 3/2 (it can be written as a fraction)

Irrational numbers: (1)An Irrational Number is a real number that cannot be written as a simple fraction. Irrational means not Rational. (2) π (Pi) is a famous irrational number.
π = 3.1415926535897932384626433832795 (and more...)
You cannot write down a simple fraction that equals Pi.
The popular approximation of 22/7 = 3.1428571428571... is close but not accurate.

8. Whole numbers are easy to remember. They're not fractions, they're not decimals, they're simply whole numbers. The only thing that makes them different than natural numbers is that we include the zero when we are referring to whole numbers. However, some mathematicians will also include the zero in natural numbers and I'm not going to argue the point. I'll accept both if a reasonable argument is presented. Whole numbers are 1, 2, 3, 4, and so on.

9. Whole Numbers: Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, … (and so on) but no fractions
Source: http://www.mathsisfun.com/whole-numbers.html

Rational Numbers:
1) A rational number is a number that can be written as a simple fraction (i.e. as a ratio).
2) Formal definition: A rational number is a number that can be in the form p/q where p and q are integers and q is not equal to zero.
Example: 1.5 is a rational number because 1.5 = 3/2 (it can be written as a fraction)
Source: http://www.mathsisfun.com/rational-numbers.html

Irrational numbers: An Irrational Number is a real number that cannot be written as a simple fraction. Irrational means not Rational.
Example: π (Pi) is a famous irrational number.
Source: http://www.mathsisfun.com/irrational-numbers.html

Integers: One of the numbers ..., -2, -1, 0, 1, 2, ....
Source: http://www.wolframalpha.com/input/?i=What+is+an+integer%3F

10. REAL NUMBERS: Nearly any number you can think of is a Real Number
e.g: 1, 12.38, -11.5

RATIONAL NUMBERS: A rational number is a number that can be written as a simple fraction
e.g: 5=5/1, 1.75=7/4

INTEGERS: Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!

WHOLE NUMBERS: Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, … (and so on)
e.g: Integers = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }

IRRATIONAL NUMBERS: An Irrational Number is a real number that cannot be written as a simple fraction.
e.g: pi (π) 3.14159....= no ratio

IMAGINARY NUMBERS: An Imaginary Number, when squared, gives a negative result.
e.g: i, 12.38i

Source: http://www.mathsisfun.com/index.htm

11. Whole numbers have no decimal or fractional part or even negatives. Whole numbers are 0,1,2,3 and so on.

Rational numbers are numbers which can be written as a ratio, which means that it can also be written as a fraction. Rational numbers are kind of related to whole numbers every whole number is a rational number. All whole numbers can be written as a fraction (which is related to ratio). An example of a rational number would be 4. 4 can also be written as a fraction (4/1).

All numbers that are not called rational numbers are called irrational numbers. Irrational numbers cannot be written as a fraction or ratio, but it can be written as a decimal. An irrational number has endless non-repeating numbers from the right of the decimal point. Irrational numbers do exist on the number line, for example, between the number 0 and 1, there are infinite numbers of irrational numbers!

Integers are like whole numbers, but they include negative numbers also. However, no fractions are allowed.

The type of numbers which we use everyday (1,15.82,3/4, -0.1) are called real numbers. Positive or negative, large or small, decimals or whole numbers are all called real numbers because they are not imaginary numbers.

How can we square a number and get a negative result? We 'imagine' that we can and it turns out that such a number, which may seem impossible, is actually useful and can solve real problems.

Sources: http://www.mathsisfun.com/whole-numbers.html
http://www.factmonster.com/ipka/A0876704.html
http://www.mathsisfun.com/definitions/real-numbers.html
http://www.mathsisfun.com/definitions/imaginary-numbers.html

12. Irrational numbers:
All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction.
An irrational number has endless non-repeating digits to the right of the decimal point. Here are some irrational numbers:
π = 3.141592…
http://www.factmonster.com/images/math/almanac/A0876704-SQROOT-1.png = 1.414213…

Source: http://www.factmonster.com/ipka/A0876704.html

13. REAL NUMBERS:
Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers.
RATIONAL AND IRRATIONAL NUMBERS:
A rational number is a number that can be written as a ratio or a fraction. An irrational number can be written as a decimal, but not as a fraction.
An irrational number has endless non-repeating digits to the right of the decimal point. An example of irrational numbers=
-Euler's number: 2.7182818284590452353602874713527
-Golden ratio: 1.61803398874989484820...
INTEGERS:
Integers include positive whole numbers, negative whole numbers, and zero.The “set of all integers” is often shown like this=
{… -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …}
WHOLE NUMBERS:
The term "whole number" is typically used in mathematics. It is frequently defined by what it does not contain: it cannot be a fraction of a number, a percentage, or have a decimal. While a number like 21.32 has a whole number portion of 21, this number is not "whole" because it contains a decimal of 0.32. Whole numbers are also often defined as non-negative integers, including zero. An example of a whole number is 15.
IMAGINARY NUMBERS:
What is i? It's the square root of -1. And it's NOT a real number. i was invented because people wanted to be able to take square roots of negative numbers, and you can't do that if you limit yourself to real numbers.So we can make an imaginary number by taking a real number like 5 and multiplying it by i. That gives us 5i. Some other imaginary numbers are:
37.3i
1.11211211111221312211131122211113213211i
Pi*i.

Sources:
http://www.virtualnerd.com/pre-algebra/real-numbers-right-triangles/real-and-irrational/define-real-numbers/real-number-definition
http://www.factmonster.com/ipka/A0876704.html
http://www.factmonster.com/ipka/A0876848.html
http://www.wisegeek.com/what-is-a-whole-number.htm
http://mathforum.org/dr.math/faq/faq.imag.num.html

14. A great repository of responses to help us recap or understand. Thank you to all respondents