Puzzle #188: 2, 0, 1, 7

Come up with arithmetic expressions that evaluate to the integers from 0 to 10 using only the digits in 2017 exactly once each and as many and as often as you need of the following: brackets, addition, subtraction, multiplication, division, unary negative (as in –2), factorial (0! = 1, 3! = 3 × 2 × 1 = 6), and simply grouping digits (as in 201 – 7).

It is possible to solve this with each expression having the digits in the order 2, 0, 1, and 7, but this is not a requirement.

Happy New Year.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 11, 2017 at noon Pacific Time. I will post the answer shortly after.