取整函数是一种常见的函数，它的形式简单，性质非常独特，在求极限、求导、求积分等的问题上都有广泛应用。应用取整函数的性质，建立一个啤酒瓶换啤酒的实数集到整数集的一个映射，将任意实数转化成整数，解决如何更加优化地买啤酒。通过把超市促销活动啤酒瓶换啤酒问题转化为数学模型，根据取整函数的性质，导出一些结果；并且对这个数学模型进行理论深入探讨与延伸，从而得到一般性的结论。结合我们得到的结论，进一步对结论进行应用，简化实际问题。
The rounding function is a common function. Its form is simple, its nature is very unique, and it is widely used in the problems of seeking limits, seeking and integrating. Applying the nature of the rounding function, a mapping of the real number set of the beer bottle to the beer to a set of inte-gers is established, and any real number is converted into an integer to solve how to optimize the beer. By transforming the problem of beer bottle change for beer in supermarket promotion into a mathematical model, some results are derived according to the nature of the rounding function; and the mathematical model is deeply explored and extended theoretically, and a general conclu-sion is obtained. Combined with the conclusions we have obtained, the conclusions are further ap-plied to simplify the actual problems.
