(I have only briefly skimmed the article, but ...) Material such as this serves to remind the reader of what they already know, and contextualize it in a way t

(I have only briefly skimmed the article, but ...) Material such as this serves to remind the reader of what they already know, and contextualize it in a way that is relevant to this article. The article begins by telling the reader, "We all know what scalars and vectors are---here they are---but have you wondered what if ...", and taking the reader beyond. The introduction which you seem to find objectionable is only a small part of a much longer article. In addition, different readers have different, mildly different notation styles. These introductory blobs inform the reader of the language in the article, and are essentially a friendly statement of definitions. A third purpose is rhetorical: readers sometimes get stuck while reading text, and these parts of the article work as anchor points where they can loop back and "synchronize" with the writer.