In the course notes for Stanford MS&E-319: https://web.stanford.edu/class/msande319/lec1.pdf
Lemma 5 is given as:
The approximation factor of the modified greedy [scheduling] algorithm is 4/3.
And gives the example:
Note that 4/3 is essentially tight. Consider an instance with $m$ machines, $n = 2m+ 1$ jobs, $2m$ jobs of length $m + 1, m + 2, · · · , 2m − 1$ and one job of length $m$.
does the above example have an error as a proof of lemma 5?
I have been thinking about it over a day.