This is totally false mathematically. Please look up the extended real number system for an example. Many branches of mathematics affix infinity to some existing number system, extending its operations consistently, and do all kinds of useful things with this setup. Being able to work with infinity in exactly the same way in IEEE754 is crucial for being able to cleanly map algorithms from these domains onto a computer. If dividing by zero were an error in floating point arithmetic, I would be unable to do my job developing numerical methods.