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Prove that the Greatest Integer Function...

Prove that the Greatest Integer Function `f : R->R ,`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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`f:R to R and f(x) = [x]`
`because " " f(2*3) = [ 2*3] = 2`
`and " " f(2*5)= [2*5] = 2`
`therefore " " f(2*3) = f(2*5)` but `2*3 ne 2*5`
`rArr f` is not one-one.
Again `1*8 in R ` and there does not exist `x in R` corresponding to it for which `f(x) = 1*8`.
`therefore f ` is not onto.
Therefore, `f` is neither one-one nor onto.
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