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An arbitrary integer is basically the same as any integer. If a math problem says: "Let n be an arbitrary integer", it means that n can be any integer. A random integer in other words.
Ordinary constant is a real constant which is same in all time but arbitrary constant is not constant at all time intervals, especially we can see arbitrary constants in integrals.For example the anti derivative of x+C is 1. Here we can replace C with any constant so C is arbitrary constant
arbitrary
It means the distance around to circle is 10.75 arbitrary units.If you were to run around the outermost edge of the circle, you would reach the starting point again after 10.75 arbitrary units.
Arbitray means nothing, the correct spelling is arbitrary