**You can’t subtract 4 from 3 **(and stay inside the natural numbers, but you can inside the integers).

**You can’t divide 3 by 4** (inside the ring of integers, but you can inside the rational numbers).

**You can’t take the square root of a negative number** (in the real numbers, but in the complex numbers you can, once you pick a branch of the square root function).

**You can’t divide by zero** (in the field of real numbers, but you may be able to do something that could informally be referred to as dividing by zero, depending on the context, by reformulating your statement, often in terms of limits).

When people say a thing cannot be done, they may mean it cannot be done in some assumed context. They may mean that the thing is difficult, and assume that the listener is sophisticated enough to interpret their answer as hyperbole. Maybe they mean that they don’t know how to do it and presume it can’t be done.

When you hear that something can’t be done, it’s worth pressing to find out in what sense it can’t be done.

**Related post**: How to differentiate a non-differentiable function