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Introduction of Real Numbers

notes

Number can be classified into Imaginary Number and Real Number.

  1. Imaginary Numbers- are those number who have i as its part eg. 12i, 98i, 71i, etc.'i' stands for iato where i= √-1 and 'i' is an imaginary constant. In the cartesian system the y-axis represents imaginary number line and the x-axis represents real number line in the complex number system. 
  2. Real Numbers- is any number without imaginary part eg. 8, `3/94,` `sqrt52,` etc. Real Number is again classified into Irrational Numbers and Rational Numbers.
  3. Irrational Numbers- these are the numbers which can not be written in `p/q` form eg. π, `sqrt55`, `sqrt1378`, etc.
  4.  Rational Numbers- they can be expressed in the form of `p/q`, where q is not eqaul to 0 eg. `6/7, 27/4, 883/95`, etc. 
  5. Integers- Integers are part of Rational Numbers. The numbers that lie on number line with a denominator of 1. They can't have decimal points. Integers can be both positive or negative eg. -45, -8, 2, 509, etc.
  6. Whole Numbers- Whole Numbers are numbers on number line starting from 0. Every number to the right side of 0 is whole number. Whole numbers are always positive eg. 1, 2, 9738, etc.
  7. Natural Numbers- Natural Numbers are all positive numbers excluding zero. Natural numbers are never in decimals eg. 1, 2, 3, 37, etc.
  8. Prime Numbers- The numbers that are divisible only by itself and 1 eg. 2, 3, 97, 101, etc.
  9. Composite Numbers- Composite Numbers can be represented as product of two Prime numbers eg. 64, 27, 119. 1 is neither Prime nor Composite number.
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Shaalaa.com | Real Numbers part 1 (Real number System)

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