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Consider the identity function, IN: N ra...

Consider the identity function, `I_N: N rarr N` defined as `I_n(x)=x forall x in N`. Show that although `I_N` is onto but `I_N+I_N: N rarr N` defined as.
`(I_N+I_N)(x)=I_N(x)+I_N(x)=x+x=2 x` is not onto

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Clearly .I_N. is onto. But .I_N+I_N. is not onto, as we can find an element 3 in the co-domain .N. such that there does not exist any .x. in the domain .N. with .(I_N+I_N)(x)=2 x=3..
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