Basic Number Theory


 
 
Concept Explanation
 

Basic Number Theory

Real Numbers (R): Is a group of numbers which can be represented on a number line. They can be classified into two categories

Rational Numbers: It is  a group of numbers which can be written in the form 

large frac{p}{q}, where ;qneq 0; and ;p;&; q ;are ;coprime

There  are certain notations to specify diffrent type of rational numbers.

  • R: Set; of; all; real ;numbers
  • R^+: Set; of; all; positive; real ;numbers
  • Z: Set; of; all; integers
  • Z^+: Set; of; all; positive;integers
  • Q: Set; of; all; rational ;numbers
  • Q^+: Set; of; all; positive; rational ;numbers
  • N^+: Set; of; all; natural ;numbers
  • The Set of Real Number contains the set of Rational and Irrational numbers.

    Q: is; a ;subset; of; R

    Z: is; a ;subset; of; Q;i.e.[.....-2,-1,0.1,2,3,4......]

    Z^+: is; a ;subset; of; Z;i.e.[0,1,2,3,4....]

    N: is; a ;subset; of; Z^+;i.e.[1,2,3,4......]

    Irrational Numbers: An irrational number is a number which cannot be written in the form

    large frac{p}{q}, where p and q are both integers and large qneq 0.Such as  large sqrt{2},sqrt{3};;and;;sqrt{5}  are irrational numbers.

    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    Which of the following prime nubes appears in the prime factorzation of 3528?

    Right Option : C
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    Explanation
    Question : 2

    If 'a' is a positive integer and 'b' is a negative integer, Which of the following is always positive?

    Right Option : C
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    Explanation
    Question : 3

    Identify the correct statement from the following options.

    Right Option : B
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    Explanation
     
     
     
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