What exactly is this 'language' for my theory computation course saying?

Question

In the manner of 2 + 2 telling me to add two and two together, what is this trying to say:

I'm not asking for an answer (I assume it's some sort of equation), just a starting place. Thanks a million.

Answer 1

$L_1$ is a set of strings; such a set is called a “language”, hence the letter $L$. (A string is a finite sequence of symbols. “Symbol” is undefined. Here you should understand that whatever a symbol is, a, b, and c are examples.)

The notation $\mathtt a^k\mathtt b^m\mathtt c^n$ means a string that has $k$ instances of a, followed by $m$ instances of b, followed by $n$ instances of c. For example, $\mathtt a^3\mathtt b^1\mathtt c^8$ is a shorthand for the string aaabcccccccc.

The notation $$L_1 = \{\mathtt a^k\mathtt b^m\mathtt c^n\mid k+m+n\ge 2\}$$ means that $L_1$ is the set of all strings that have some a's followed by some b's followed by some cs, where the number of a's plus the number of b's plus the number of c's is at least $2$.

For example, $L_1$ includes the string aabbbc because it can be understood as $\mathtt a^2\mathtt b^3\mathtt c^1$ and $2+3+1\ge 2$. But the string bbaabc is not in $L_1$ because it doesn't have the as before the bs before the cs.

Note that $k,m,$ and $n$ could be zero. In particular, bb is in $L_1$ because it is $\mathtt a^0\mathtt b^2\mathtt c^0$ and $0+2+0\ge 2$.