In Math, a base is the number of numbers used to describe the mathematical system. For example, a base 2 system is called binary and uses 0 and 1; a base 10 system is a decimal system, and uses the current standard of ten numbers ranged from 0 to 10.
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A real world example of what? Math in general? Geometry nets? Name the math concept and it'll be easier for readers to give you a real world example.
A Mirror
A fjord is a real world example of a fjord! They exist in the real world.
Unless you are an electrical engineer or a math teacher, every number you will ever use in a real world situation will be a real number.
2 is a real world prime number.