Continuous mapping is a mathematical concept that describes a function or mapping between two sets, where small changes in the input result in small changes in the output. In other words, it means that the function or mapping is unbroken or uninterrupted.
Continuous mapping is important in science because it allows us to model and understand real-world phenomena that involve gradual changes, such as weather patterns, population growth, and physical processes. It also provides a basis for mathematical analysis and prediction.
Examples of continuous mapping in science include the relationship between temperature and pressure in a gas, the growth of bacteria in a culture, and the movement of tectonic plates on Earth's surface. Other examples include the flow of water in a river, the spread of a disease in a population, and the changes in a person's blood sugar levels over time.
The main difference between continuous mapping and discontinuous mapping is that continuous mapping describes a function or mapping that is uninterrupted, while discontinuous mapping describes a function or mapping that has breaks or gaps. In other words, small changes in the input of a continuous mapping result in small changes in the output, while small changes in the input of a discontinuous mapping can result in large changes in the output.
Continuous mapping can be visualized using a graph or plot, where the input is represented on the x-axis and the output is represented on the y-axis. In a continuous mapping, the graph will show a continuous line or curve, without any breaks or gaps. This allows us to see the relationship between the input and output and how small changes in the input affect the output.