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

Related post:

complement of a set symbol

Reversal law of inverse

difference of two set

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