Dear sir, I have this question about the domain, range and co domain of a function.
What is the correct definition for the co domain and what is the importance of it ?
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Codomain Y is a set stated by the definition of a function such that all outputs of the function need to be within it , in other words it is a set of all possible outputs. Range R is the set of all outputs of a function and which can be determined by the relation and domain of the function. Therefore by definition R should be a subset of Y. If R = Y function maps it’s domain onto codomain , if R ⊂ Y function maps it’s domain into codomain.
To get a better insight of the issue we can consider probability function because it has practical importance and we can clearly see the difference of the two sets . Here the domain is Event space and codomain is the set [0,1] but range is only particular values within the set [0,1]. In the case of tossing a coin once range is the set {0,1/2 , 1} .
Thank you very much sir.
Actually it should be tossing a fair coin not just a coin.
Of course 😊