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Erm, wouldn't that be the second derivative?

d(users)/dt would be the rate of change of users. That can only be negative if the amount of users decreases, ie through bannings.

You're thinking of the second derivative, d^2(users)/dt^2, which is the rate of change of the rate of increase of users. If that is negative, it means that the growth has slowed down, as in your example with February and March.

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I was asking about the second derivative; if d(users)/dt wasn't constant, then d^2(users)/dt2 is nonzero and eternal september risk is fairly high (assuming HN isn't shrinking). If you assume idealized user growth (which doesn't happen -- there are so many people in the end that would care to either join HN or troll HN), then eternal september is actually guaranteed if d^2(users)/dt2 > 0, since there will come a time t when (new users) > (old users).

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