Days Gone By

Should auld acquaintance be forgot and never brought to mind? Should auld acquaintance be forgot, and days of auld lang syne? (Hint: Assume the opposite and try to derive a contradiction.)

Dialogue Concerning Birthdays

"Happy birthday, Synthia!"

"Why," mused Synthia, "do we celebrate birthdays? I fail to see anything special about the calendar day on which a person's age-in-calendar-years passes an integer. Are things supposed to be different now that it's been seven-point-five-seven-four times ten-to-the-eighth seconds since my birth, rather than seven-point-five-seven-three?"

Quiana suppressed a groan. Somehow she had been expecting Synthia to say something "normal," like Thanks! But knowing Synthia, it would have been unusual if she had done so: relative to Quiana's state of knowledge of her friend, this—the general style, though not, of course, the specific questions—was the normal response.
Most people learn during their study of the differential and integral calculus that the derivative of the natural logarithm ln x is the reciprocal function 1/x. Indeed, sometimes the natural logarithm is defined as $\int_1^x \frac{1}{t}\,dt$. However, on observing the graphs of ln x and 1/x, the inquisitive seeker of knowledge can hardly fail to notice a disturbing anomaly: