Many people use "let, let's and lets" in conversation What's the difference between them?
I find the distinction that MacMillan makes between not to mention and the supposedly synonymous let alone and still/much/even less useful: The phrases let alone and still/much/even less reinforce a negative or unlikely statement that precedes them. The still/much/even less constructs reinforce the negativity of the preceding phrase by subtraction -- Negative statement, still/much/even less ...
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.
People: What Is the 'Let Them' Theory? Here’s Why the Self-Help Motto Is Taking Over the Internet
There are over 11,000 videos on TikTok using the hashtag "let them theory" Nathan Congleton/NBC via Getty ; Hay House LLC Mel Robbins' "let them" theory has taken over the internet. The self-help guru ...
What Is the 'Let Them' Theory? Here’s Why the Self-Help Motto Is Taking Over the Internet
Yahoo: What is the 'let them' theory? Breaking down the phrase popularized by Mel Robbins that's all about boundaries.
What is the 'let them' theory? Breaking down the phrase popularized by Mel Robbins that's all about boundaries.
MSN: 2025 was dominated by the Let Them Theory. 2026 will be Let Them Be Petty.