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Hey I was reading Susanna Discrete book and I came across her definition of One-to-One function:

Let F be a function from a set X to a set Y. F is one-to-one (or injective) if, and only if, for all elements x

if F(x

or, equivalently, if x

Symbolically,

F: X → Y is one-to-one ⇔ ∀x 1 ,x 2 ∈ X,if F(x

But I am not sure if I fully understand the definition. Here is my interpretation of the definition:

A function is said to be one-to-one if and only if,

if f(x

e.g if f(x

x

Since, the co-domain 3 is being pointed by a two non-distinctive domain 1 then it said to be a one-to-one function.

Let F be a function from a set X to a set Y. F is one-to-one (or injective) if, and only if, for all elements x

_{1}and x_{2}in X,if F(x

_{1}) = F(x_{2}),then x_{1}= x_{2},or, equivalently, if x

_{1}≠ x_{2},then F(x_{1}) ≠ F(x_{2}).Symbolically,

F: X → Y is one-to-one ⇔ ∀x 1 ,x 2 ∈ X,if F(x

_{1}) = F(x_{2}) then x_{1}= x_{2}.But I am not sure if I fully understand the definition. Here is my interpretation of the definition:

A function is said to be one-to-one if and only if,

if f(x

_{1}) and f(x_{2}) are the same then x_{1}=x_{2},e.g if f(x

_{1})=f(x_{2})=3, thenx

_{1}= x_{2}= 1Since, the co-domain 3 is being pointed by a two non-distinctive domain 1 then it said to be a one-to-one function.

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