I&#x27;m afraid you have some basic confusion with mathematical concepts, including &quot;mapping&quot;, &quot;irrational&quot;, &quot;complex&quot;, and &quot;infinity&quot;.<p>So, after you define x+1 and x+i, now what?  Also please bear in mind that &quot;infinity&quot; is neither real nor complex: if you have a well-defined mapping into complex numbers, then by definition, it never maps to infinity.<p>(Yes, there are some &quot;functions&quot; like y = 1&#x2F;x that &quot;maps to infinity&quot;, but it&#x27;s simply mathematicians being lazy and abusing notations because everybody around them understands what&#x27;s going on.)