Question

Show me greatest integer function is neither one one nor onto

Answer 1

Hey friend,Harish here.

Here is your answer:

Let the greatest integer function be:

f :  R → R, Which is given by,

f(x) = [x]

We know that: f(1.5) = [1.5] = 1 ; f(1.6) = [1.6] = 1. 

∴ f(1.5) ≠ f(1.6)  & f is not one to one function.

Now, Let 0.5 ∈ R.

We know that, 

f(x) = [x] is always an integer. Thus, there does not exist any an element x ∈ R such that f(x) = 0.5.

∴ f is also not onto.

Hence the greatest integer function is neither one - one, nor onto.
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Hope my answer is helpful to you.