Number Theory - Its a study of numerical of math such as Rational and Irrational Numbers, Natural Numbers, Whole numbers, significant Figures, Prime Numbers, Fractions etc.
And the basic of number theory lies in understanding natural numbers, whole numbers, fractions and rational-irrational numbers. They are defined as follows.
* Natural numbers - The countable numbers are called Natural Numbers.
* Whole numbers - The set of whole numbers is the set of natural numbers along with zero. so
W = the set of whole numbers = 0, 1, 2, 3, ............
* Fractions - Fraction is an equal part of one whole object.
* Rational numbers - The rational numbers can be expressed as terminating or recurring decimals.
* Irrational numbers - Numbers which are not rational are called irrational numbers.
Natural numbers :
Therefore 1 is the smallest or least of all natural numbers.
The highest natural number cannot be said because Natural numbers are infinite.
The set of Natural numbers is a subset of Rational numbers
Whole numbers :
Properties of Whole numbers
It is advisable to use a number line inorder to understand the properties of whole numbers.
1. Number 3 < 5 and the number 3 is to the left of the number 5. Hence of an two numbers on a number line, the smaller number is to the left of the greater number.So too,of any two numbers on a number line the number to the left of the other number, is the smaller of the two.
2 . There is no whole number to the left of zero on the number line.So zero is the smaller number than each of the numbers to its right on the number line.That means 0 is the smallest or least of the whole numbers.
3. A whole number which is greater than a given whole number by 1 is said to be a successive whole number. 1 is the successive whole number to 0.Every whole number has one successor.
4. There is no whole number left to zero.hence 0 is not a successive whole number of any whole.
Fractions :
A part of a whole when it is divided into equal parts is a fraction.
Set of Fraction is a subset of the set of Rational Numbers
Eg : The whole Pizza is divided into 5 equal parts,then one part of it is expressed as 1/5
Rational numbers :
The rational numbers can be expressed as terminating or recurring decimals. Decimal fraction has denominator as 10 or a power of 10. A recurring decimal is denoted by placing dots or a bar over recurring digits.
Irrational numbers :
Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. We can obtain infinite number of irrationals between two irrational numbers.
And the basic of number theory lies in understanding natural numbers, whole numbers, fractions and rational-irrational numbers. They are defined as follows.
* Natural numbers - The countable numbers are called Natural Numbers.
* Whole numbers - The set of whole numbers is the set of natural numbers along with zero. so
W = the set of whole numbers = 0, 1, 2, 3, ............
* Fractions - Fraction is an equal part of one whole object.
* Rational numbers - The rational numbers can be expressed as terminating or recurring decimals.
* Irrational numbers - Numbers which are not rational are called irrational numbers.
So math answers for number theory is as follows...
Natural numbers :
Therefore 1 is the smallest or least of all natural numbers.
The highest natural number cannot be said because Natural numbers are infinite.
The set of Natural numbers is a subset of Rational numbers
Whole numbers :
Properties of Whole numbers
It is advisable to use a number line inorder to understand the properties of whole numbers.
1. Number 3 < 5 and the number 3 is to the left of the number 5. Hence of an two numbers on a number line, the smaller number is to the left of the greater number.So too,of any two numbers on a number line the number to the left of the other number, is the smaller of the two.
2 . There is no whole number to the left of zero on the number line.So zero is the smaller number than each of the numbers to its right on the number line.That means 0 is the smallest or least of the whole numbers.
3. A whole number which is greater than a given whole number by 1 is said to be a successive whole number. 1 is the successive whole number to 0.Every whole number has one successor.
4. There is no whole number left to zero.hence 0 is not a successive whole number of any whole.
Fractions :
A part of a whole when it is divided into equal parts is a fraction.
Set of Fraction is a subset of the set of Rational Numbers
Eg : The whole Pizza is divided into 5 equal parts,then one part of it is expressed as 1/5
Rational numbers :
The rational numbers can be expressed as terminating or recurring decimals. Decimal fraction has denominator as 10 or a power of 10. A recurring decimal is denoted by placing dots or a bar over recurring digits.
Irrational numbers :
Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. We can obtain infinite number of irrationals between two irrational numbers.
