Let's denote by Mi the i$-$th Turing machine, and define a function f$()$ as follows:

$$ If Mi halts with an empty input, then f$($i$)=$ the number of steps performed before halting.

$$ Otherwise, f$($i$)=0.$

Also, let

g$($j$)=$ max

ij

f$($i$).$

Prove that g$()$ is not computable.Let's denote by Mi the i$-$th Turing machine, and define a function $f(*)$ as follows:

If Mi halts with an empty input, then $f(i)=$ the number of steps performed before halting.

Otherwise, $f(i)=0.$

Also, let $g(j)$:$=ma{x}_{i}jf(i).$

Prove that $g(*)$ is not computable.