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Every course I've taken so far (differential calculus through multivariable calculus, linear algebra, a proofs writing course, etc) always defined the Reals with just they symbol ℝ and we always included infinity and negative infinity.

Were all of my teachers just using ℝ as shorthand for ℝ U {+infinity, -infinity} or is there some fundamental difference?

Actually, I shouldn't ask on this forum what my teachers were doing, but rather, is it commonplace to use ℝ as shorthand for the extended reals?