<P> In real analysis, the symbol ∞ (\ displaystyle \ infty), called "infinity", is used to denote an unbounded limit . x → ∞ (\ displaystyle x \ rightarrow \ infty) means that x grows without bound, and x → − ∞ (\ displaystyle x \ to - \ infty) means the value of x is decreasing without bound . If f (t) ≥ 0 for every t, then </P> <Ul> <Li> ∫ a b f (t) d t = ∞ (\ displaystyle \ int _ (a) ^ (b) f (t) \, dt = \ infty) means that f (t) does not bound a finite area from a (\ displaystyle a) to b (\ displaystyle b) </Li> <Li> ∫ − ∞ ∞ f (t) d t = ∞ (\ displaystyle \ int _ (- \ infty) ^ (\ infty) f (t) \, dt = \ infty) means that the area under f (t) is infinite . </Li> <Li> ∫ − ∞ ∞ f (t) d t = a (\ displaystyle \ int _ (- \ infty) ^ (\ infty) f (t) \, dt = a) means that the total area under f (t) is finite, and equals a (\ displaystyle a) </Li> </Ul> <Li> ∫ a b f (t) d t = ∞ (\ displaystyle \ int _ (a) ^ (b) f (t) \, dt = \ infty) means that f (t) does not bound a finite area from a (\ displaystyle a) to b (\ displaystyle b) </Li> <Li> ∫ − ∞ ∞ f (t) d t = ∞ (\ displaystyle \ int _ (- \ infty) ^ (\ infty) f (t) \, dt = \ infty) means that the area under f (t) is infinite . </Li>

Where did the idea of infinity come from