section_path: Mathematics/Calculus/Real analysis
section_name: Real analysis
paragraph_text: Real analysis
  
  In real analysis, the symbol ∞ {\displaystyle \infty }, called "infinity", is used to denote an unbounded limit. The notation x → ∞ {\displaystyle x\rightarrow \infty } means that x {\displaystyle x} increases without bound, and x → − ∞ {\displaystyle x\to -\infty } means that x {\displaystyle x} decreases without bound. For example, if f (t) ≥ 0 {\displaystyle f(t)\geq 0} for every t {\displaystyle t}, then
  
  Infinity can also be used to describe infinite series, as follows:
  
  In addition to defining a limit, infinity can be also used as a value in the extended real number system. Points labeled + ∞ {\displaystyle +\infty } and − ∞ {\displaystyle -\infty } can be added to the topological space of the real numbers, producing the two-point compactification of the real numbers. Adding algebraic properties to this gives us the extended real numbers. We can also treat + ∞ {\displaystyle +\infty } and − ∞ {\displaystyle -\infty } as the same, leading to the one-point compactification of the real numbers, which is the real projective line. Projective geometry also refers to a line at infinity in plane geometry, a plane at infinity in three-dimensional space, and a hyperplane at infinity for general dimensions, each consisting of points at infinity.