/sci/ - Science & Math

Here is a good example of vagueness of the word "diverges". This definition seems to imply that the only sequences that are divergent are those that go to infinity. While in standard mathematics, the sequence -1, +1, -1, +1, ... (alternating signs) is a divergent sequence which doesn't explode. So is the sequence -1, -2, -3, .... which should probably converge to -infinity. is this not a divergent sequence according to you? What is a divergent sequence?