The author has taken the (correct) 'don't go there', which is a correctly formed second person imperative, and turned it into a verb, and the Let's is turned into an injunction for us to "don't go there".
Forbes: Beauty Bio-Hack In Med Spas: Advice For Spa Owners And Practitioners
In an era where the intersection of technology and personal health is more pronounced than ever, the beauty industry is undergoing a significant metamorphosis. As someone who runs a med spa, I've seen ...
Recently, I talked to a native speaker about the proper usage of the word “kindly”. I frequently use phrases like “kindly let us know whether you agree with the suggested approach” in business let...
Let is used for assigning a mathematical value to a symbol. "Suppose N is finite" has meaning while "Let N be finite" doesn't make sense. On the other hand, both "Let n = 1" and "Suppose n = 1" are acceptable, though the former is preferred. I can see a situation when you might use the latter.
meaning - When do we use "suppose" and when "let"? - English Language ...
grammar - "Let's not go there" or "'let's don't go there" - English ...
I think that "Let A be a set, let B be a group, and let C be a number." is the most formal phrasing. Since this is a mathematically formal usage, I think that would be preferred, but I don't think any of the phrases you presented are wrong, and "Let A be a set, B a group, and C a number." is shorter and more succinct. On a separate note, we have a sister site for Math you might consult.