The other day after presenting a simple 2-approximation I tried to show a complicated, improved 3/2 approximation, but a factor of 2 somehow disappeared along the way, and I ended up with a proof that my more complicated algorithm was a 3-approximation! That happens to me all the time, and, strangely, it always seems to be the 2's and the 1/2's that disappear. The 5's and 7' are much more serious and responsible. Once they come, they stay. They don't go away without reason.
2's look naive and honest, but they are immature (have you noticed how they always come up at the first half-baked attempt to examine something?) and one should beware of their taste for pranks.