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@ -143,5 +143,5 @@ print(x) # -> 2.220446049250313e-16
```
One might think that this constitutes an infinite loop. To the contrary, the loop will be left in finite time. The result for double precision is $x \approx 2\times 10^{-16}$ (import sys ; print(sys.float_info.epsilon)). eps is the smallest number with $1+$eps$>1$, and is the \quoting{machine accuracy}. Rounding errors of this order of magnitude occur on a regular basis. For example, Python calculates $\sin{\pi} \approx 1.2246\times 10^{-16}$ (import math ; print(math.sin(math.pi)) # -> 1.2246467991473532e-16). It shall be mentioned hat the machine accuracy for double precision is exactly eps $= 2^{-52}$, since 52 bits (plus one bit for the sign) are used for the mantissa. This rounding error might appear to be small and negligible. However, if further calculations are performed with rounded numbers, the rounding errors can accumulate with each calculation and grow to a significant value.
One might think that this constitutes an infinite loop. To the contrary, the loop will be left in finite time. The result for double precision is $x \approx 2\times 10^{-16}$ (import sys ; print(sys.float_info.epsilon) ). eps is the smallest number with $1+$eps$>1$, and is the \quoting{machine accuracy}. Rounding errors of this order of magnitude occur on a regular basis. For example, Python calculates $\sin{\pi} \approx 1.2246\times 10^{-16}$ (import math ; print(math.sin(math.pi)) ). It shall be mentioned hat the machine accuracy for double precision is exactly eps $= 2^{-52}$, since 52 bits (plus one bit for the sign) are used for the mantissa. This rounding error might appear to be small and negligible. However, if further calculations are performed with rounded numbers, the rounding errors can accumulate with each calculation and grow to a significant value.