In a large company, (1)……… people is about as common as using a gun or a switch blade to (2)………an argument. As a result, most managers have little or no experience of firing people, and they find it emotionally traumatic; as result, they often delay the act interminably, much as an unhappy spouse will prolong a bad marriage. And when they firing is done, it’s often done clumsily, with far worse side effects than are necessary.
Do the world class software organization have a different way of firing people? No but they do the deed swiftly, humanely, and professionally. The key point here is to view the fired employee as a “failed product” and to ask how the process (3)…… such a phenomenon in the first place.
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: