Greek letter paradox

The Greek letter paradox is seeing the same symbol in two contexts and assuming it means the same thing. Maybe it's used in many contexts, but I first heard it in the context of comparing statistical models.

I used the phrase in my previous post, looking at

exp(5t) + t exp(5t)

and

exp(4.999 t) + exp(5.001 t).

In both cases, is the coefficient of a term equal to or approximately equal to exp(5t), so in some sense means the same thing in both equations. But as that post shows, the value of depends on its full context. In that sense, it's a coincidence that the same letter is used in both equations.

When the two functions above are solutions to a differential equation and a tiny perturbation in the same equation, the values of and are very different even though the resulting functions are nearly equal (for moderately small t).

The post Greek letter paradox first appeared on John D. Cook.