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What is Real Number? Properties & Types of Real Numbers with Example


What is Real Numbers?

When two numbers like rational or irrational numbers are combined together then this combination is named as the real numbers. It could be both either positive or negative and they could be given by the symbol R. The numbers like natural, decimals or even fractions could be given under the category of real numbers.

Type of Real Numbers

Further, let us see how to classify the real numbers.

  • Natural numbers – they are given as the simple numbers like 1, 2, 3, 4, …. and so on.
  • Whole numbers – there are a few number series that start with zero as well and it is called the whole numbers 0, 1, 2, 3, 4, …
  • Integers – the negative of natural numbers and whole numbers together called as integers like -3, -2, -1, 0, 1, 2,
  • Rational Numbers – if there is some number that could be given in the form of p/q where q cannot be equal to zero then it is a rational number.
  • Irrational Numbers – if there is some number that could not be given in the p/q form then it is called as the irrational numbers. They are non-terminating and generally non-repeated in nature.

Properties of Real Numbers

  • First is Commutative property that could be given as m + n = n + m for addition and m.n = n.m for multiplication.
  • There is Associate property whose general form could be given as m + (n + r) = (m + n) + r for addition(mn) r = m (nr) for multiplication
  • There is distributive property whose general form could be given as m (n + r) = mn + mr and (m + n) r = mr + nr
  • There is identity property whose general form for addition could be given as – m + (- m) = 0


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