# Floating-point Numbers Aren't Real

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- | Floating-point numbers are not real numbers in the mathematical sense. Real numbers have infinite precision; floating-point numbers have fixed precision, and resemble "badly-behaved" integers. If you have access to a 32-bit platform with single-precision IEEE floating-point, like '''float''' in C++ on Windows, assign 2147483647 (the largest signed integer) to a float variable ('''x''', say), and print it. You'll see 2147483648! | + | Floating-point numbers are not real numbers in the mathematical sense. Real numbers have infinite precision; floating-point numbers have fixed precision, and resemble "badly-behaved" integers. If you have access to a 32-bit platform with single-precision IEEE floating-point, like '''float''' in C++ on Windows, assign 2147483647 (the largest signed integer) to a float variable ('''x''', say), and print it. You'll see 2147483648. Now print x - 64. Still 2147483648. Now print x-65 and you'll get 2147483520! |

## Revision as of 16:09, 14 December 2008

Floating-point numbers are not real numbers in the mathematical sense. Real numbers have infinite precision; floating-point numbers have fixed precision, and resemble "badly-behaved" integers. If you have access to a 32-bit platform with single-precision IEEE floating-point, like **float** in C++ on Windows, assign 2147483647 (the largest signed integer) to a float variable (**x**, say), and print it. You'll see 2147483648. Now print x - 64. Still 2147483648. Now print x-65 and you'll get 2147483520!