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Some Scheme implementations, specifically those that follow the IEEE floating–point standards, distinguish special number objects called positive infinity, negative infinity and NaN.
Positive infinity is regarded as an inexact real (but not rational) number object that represents an indeterminate number greater than the numbers represented by all rational number objects. Negative infinity is regarded as an inexact real (but not rational) number object that represents an indeterminate number less than the numbers represented by all rational numbers.
A NaN is regarded as an inexact real (but not rational) number object so indeterminate that it might represent any real number, including positive or negative infinity, and might even be greater than positive infinity or less than negative infinity.