Mathematics in real life is continuous, not so on a computer. Article based on FastAI Computational Linear Algebra course1.
Course page
Source: https://tzeny.ddns.net:4430/Tzeny/fastai_numerical-linear-algebra/blob/master/nbs/1.%20Why%20are%20we%20here.ipynb
Floats
Floating point numbers have a maximum and a minimum: 1.79 * 10308and as small as 2.23 * 10−308.
There are uneven gaps between numbers.
Machine epsilon
The error between 1 and the next larger number: ϵmachin**e = 2−53 ≈ 1.11 * 10−16 (as defined by IEEE)
I will stop maintaing course notes for this course as the Jupyter Notebooks are more than adequate.