Natural Numbers can mean either Counting Numbers {1, 2, 3, ...}, or Whole Numbers {0, 1, 2, 3, ...}, depending on the subject. Integers. Integers are like whole numbers, but they also include negative numbers... but still no fractions allowed! So, integers can be negative {-1, -2,-3, -4, -5, ... }, positive {1, 2, 3, 4, 5, ... }, or zero {0} We can put that all together like this: Integers = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
An application-programming interface (API) is a set of programming instructions and standards for accessing a Web-based software application or Web tool. A software company releases its API to the public so that other software developers can design products that are powered by its service. For example, Amazon.com released its API so that Web site developers could more easily access Amazon's product information.
An application programming interface (API) is (as the name suggests) an interface for your application to use code that does not belong to your application (usually a library). Usually, an API is comprised of a set of function/method calls that can be made to the library by your application. All system calls together constitute an API that the operating system (kernel) provides to applications that run on that platform.