Question

Show that the signum function `f: R to R` defined by
`f(x) ={ [-1 if x lt 0], [0 if x=0], [1 if x gt 0]}`
is neither one-one nor onto.

Answer 1

Clearly `f(2) =1 "and " f(3) =1`
Thus `f(2) =f(3) " while " 2 ne 3`
`:. ` f is not one-one
Range `(f) ={1 ,0, -1} sub R.`
So f is onto.
Hence f is neither one-one nor onto.