What are the well-known examples of almost integers? 

High powers of the golden ratio are well-known examples of almost integers because as the power of the golden ratio increases, the resulting number gets closer and closer to an integer. The golden ratio, denoted by the symbol φ (phi), is approximately equal to 1.618. When this value is raised to a high power, the decimal part becomes very small, making it almost an integer. This property of the golden ratio is often seen in various mathematical and natural phenomena, such as in the spirals of certain plants and the proportions of ancient Greek architecture.