Question

what is the difference between (-infinity,infinity) and all real numbers R?

Answer 1

Answer:

There is no difference: R=]−∞,+∞[. Writing it like this serves to get you used with the symbol ∞, I guess (mostly psychological reasons?). Also, there will be a time when you'll need to use concepts dealing with the extended real line, so it will be natural to talk about:

]−∞,+∞],[−∞,+∞[, and [−∞,+∞].