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Prove that the greatest integer function...

Prove that the greatest integer function `f : R rarrR` given by `f(x) =[x]` is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

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We have `f(0.5) = [0.5] = 0` and
f(0.75) = [0.75] = 0
therefore` Both 0.5 and 0.75 are mapped to 0
`therefore` f is not one-one
Since the value of f(x) are all integers, non-integer real numbers can.t have pre-images.
`therefore` f is not onto.
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