I struggled to understand the Cantor's diagonal argument, but I have some problems comprehending the following:By construction, $s$ differs from each $s_n$, since their $n^{th}$ digits differ (highlighted in the example). Hence, $s$ cannot occur in the enumeration.Can someone explain why the built sequence $s$ cannot occur in the enumeration? I can imagine it somehow recursively that if we add it to $s_n$, we can pick another sequence with the same construction pattern and we can repeat these steps forever. However, I want to know if this is sufficient as a proof or there is some kind of other explanation.
Explanation of Cantor's diagonal argument?
set theory
It's actually more trivial. Suppose that $s$ occurs in the enumeration. Then it occurs at some specific index. Let's call this index $n$. This means that $s = s_n$. But this is impossible, because $s$ and $s_n$ differ in the $n$th digit.