I am an incoming math PhD student in the US. I am thinking of starting a math blog. The intended audience is myself plus maybe other math graduate students.
I am a little concerned about citations to avoid plagiarism. Of course if a theorem or proof comes from a paper, I need to cite it. What about theorems and proofs coming from textbooks. For example, say I give a definition of a group, which appears in virtually all standard textbooks in introductory algebra.
I guess the latter case will happen more frequently since my blog is mostly entry level graduate material math that you can find in many textbooks.
Questions:

If a theorem or proof comes from a textbook, can I assume that it is considered common knowledge, with respect to the targeted audience, and just state and prove the theorem?

At what point does a theorem or proof stop becoming common knowledge, maybe it only appears in some very advanced textbooks?