I understand that a continued fraction is given by iterating $; x \\rightarrow floor(x) , \\frac{1}{x - floor(x)} ;$ , but how can I reverse this? Is there a way to get from a continued fraction back to the number that generates it? Is there a formula  that takes a list of numbers and returns the number that generates it?

Since $; \[3; 1$ = $4$ ;\], it's impossible to completely reverse it.

I've seen the $; a\_0 + \\frac{1}{a\_1 + \\frac{1}{a\_2 + ...}} ;$ thing, but with the "..." on the right, I'm not sure how to turn it into an explicit formula.
>Is there a way to get from a continued fraction back to the number that generates it?

a continued fraction is a number. that's the whole point, it's the same number you started with, just written differently. if you want a decimal expansion, do long division.
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