A periodic function is a mathematical function that repeats its values at regular intervals. This means that the function will have values that are repeated after a certain amount of input or time.
1-periodicity means that a function repeats its values after 1 unit of input or time. In other words, the function will have a period of 1. This can also be referred to as a cycle or wavelength of 1.
To determine if a function is 1-periodic, you can graph the function and look for a repeating pattern that occurs after 1 unit of input or time. Alternatively, you can also check if the function satisfies the equation f(x) = f(x+1), meaning that the function's output at x is equal to its output at x+1.
Some real-life examples of 1-periodic functions include the movement of a pendulum, the tides of the ocean, and the rotation of the Earth on its axis. These phenomena have a repeating pattern that occurs after 1 unit of time.
1-periodicity is a specific type of periodicity where the function repeats its values after 1 unit of input or time. Other types of periodicity can have different periods or cycles, such as 2-periodicity or 3-periodicity. Additionally, some functions may have irregular or non-repeating patterns, making them non-periodic.