volume_mute
x + (+∞) for x ∈ ℝ
publish date: 2026/05/23 22:07:21.551458 UTC
volume_mute
For any real number \(x \in \mathbb{R}\), what is \(x + (+\infty)\)?
Correct Answer
\(+\infty\)
Explanation
\(x + (+\infty) = +\infty\) for any finite \(x \in \mathbb{R}\). Adding any finite number to \(+\infty\) still gives \(+\infty\). Intuitively: adding a finite quantity to an unboundedly large quantity leaves it unboundedly large. Similarly, \(x + (-\infty) = -\infty\).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012