Sure, but what is d_\infty? What is the set \infty? What does the question mean by “every real number can be represented by”? There’s nothing distinguishing d_1d_2… with d_1 times d_2 since we normally denote the product by writing the variables next to each other

I think this question is very poorly worded

The pythagorean theorem works in any complex hilbert space

The lengths you can construct are exactly the numbers which are composed of 1, addition, subtraction, multiplication, division, and square roots