Acworth is a city in Cobb County, Georgia, United States. It is part of the Atlanta metropolitan area. As of the 2020 census, this city had a population of 22,440, up from 20,425 in 2010. Acworth is located in the foothills of the North Georgia mountains along the southeastern banks of Lake Acworth and Lake Allatoona on the Etowah River. Unincorporated areas known as Acworth extend into Bartow, Cherokee, and Paulding counties.
Acworth is often referred to as "the Lake City" because of its proximity to Lake Allatoona and Lake Acworth.
I suppose that it is because we are in extended real numbers. But the definition of a limit when ##x_0 = \infty## and let's say ##L=\infty## is different. Why are these definitions equivalent? Isn't the key that ##U_{\varepsilon}(\infty)=\left(\frac {1}{\varepsilon},\infty\right)##?