Hey I was reading Susanna Discrete book and I came across her definition of One-to-One function:(adsbygoogle = window.adsbygoogle || []).push({});

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, then

x_{1}= x_{2}= 1

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.

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# One-to-One Function

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