Problem $2$: Python $($Chapra$,$ Problem $4\mathrm{.}4).$

For computers, the machine epsilon $$ can also be thought of as the smallest number that when added to

one gives a number greater than $1.$ An algorithm based on this idea can be developed as

Step $1$: Set $=1.$

Step $2$: If $1+$ is less than or equal to $1,$ then go to Step $5.$ Otherwise go to Step $3.$

Step $3$: $=\frac{}{2}$

Step $4$: Return to Step $2$

Step $5$: $=2$

Write your own Python script based on this algorithm to determine the machine epsilon. Validate the result

by comparing it with the value computed with the Python NumPy command, np$.$ finfo $($float$).$ eps.

If the values are different, consider why that might be$.$