And computers have a hard time with that. Take the following example code:

  #include <math.h>
  #include <stdio.h>
  #include <stdlib.h>
  double f(const double x) {
      return pow(x, 1000) / pow(x, 998);
  }
  int main(int argc, char* argv[]) {
      if(argc != 2) {
          fprintf(stderr, "Usage: %s x\n", argv[0]);
          exit(1);
      }
      const double x = atof(argv[1]); // demo code without error checking
      printf("x = %g, f(x) = %g\n", x, f(x));
      exit(0);
  }

compile with

  gcc -Wall -g -o test test.c -lm

and run it

  petschge@localhost:~$ ./test 0
    x = 0, f(x) = -nan
  petschge@localhost:~$ ./test 1
    x = 1, f(x) = 1
  petschge@localhost:~$ ./test 2
    x = 2, f(x) = 4

The fun thing is, when you compile with

  gcc -Wall -O3 -ffast-math -g -o test2 test.c -lm

you actually get

  petschge@localhost:~$ ./test2 0
    x = 0, f(x) = 0

That's exactly what i'm saying.