Multiplicative inverse of real number: The element ” 1 / a ” is called Multiplicative inverse of real number ” a ”
Symbolically:
∀ a ∈ R ( a ≠ 0) , ∃ 1 / a ∈ R
such that
a × 1 / a = 1/ a ×a =1
∀ Read as ( for all )
a ∈ ( means is a part of real number ) R ( a ≠ 0)
∃ ( means there exist) 1 / a ∈ R
Example:
7, 1/7 ∈ R ⇒ 7 × 1 / 7 = 1 = 1 /7 × 7
Multiplicative identity of real number:
The element ” 1 ” is called multiplicative identity of real number
Symbolically:
∀ a ∈ R , ∃ 1 ∈ R
such that
a × 1 = 1 ×a =a
Example:
5 ∈ R ⇒ 5 × 1 = 5 = 1 × 5
Commutative property of real number w.r.t multiplication
The product of two real numbers is independent of order in which they are multiplied
Symbolically:
∀ a, b ∈ R , a.b = b.a
Example:
2,4 ∈ R this implies that 2 × 4 = 8 = 4 ×2
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