Talk:Exponentiation/Archive 2023

What do the dots mean please?
I am a modestly intelligent UK beginner wishing to understand from Wikipedia about Exponentiation, as a stepping-stone to understanding what logarithms are and why one wants them. Simple, eh? To me, the lede paragraph of this article is clearly well-constructed, but becomes meaningless when the special dots start to be introduced into the mathematical examples. For instance, in the first example $$b^n = \underbrace{b \times b \times \dots \times b \times b}_{n \text{ times}}.$$ I understand that the three dots represent a kind of space-filler, expressing the variable number of possible multiplications of the base represented by the integer n. Are they, therefore, within the normal range of algebraic notation, or are they an extraneous usage (meaning something like "extended to the corresponding number"), rather like the dots used to transcribe unreadable letters in manuscript texts - ? Taking the latter to be the case, I make sense of the next examples on the same principle, but then I come to a puzzling set of equations where the single dot is employed:"'In other words, when multiplying a base raised to one exponent by the same base raised to another exponent, the exponents add. From this basic rule that exponents add, we can derive that $b^0$ must be equal to 1, as follows. For any $n$, $b^0 \cdot b^n = b^{0+n} = b^n$. Dividing both sides by $b^n$ gives $b^0 = b^n / b^n = 1$.'" Here, in the formulation $$b^0 \cdot b^n = b^{0+n} = b^n$$ the single dot does not stand for a missing number, but apparently represents a mathematical operation or relationship (?addition or multiplication, or merely juxtaposition or sequence?) which has not been explained to the reader.

The problem gets worse when one comes to the formulation in the next lines, $$ (b^1)^3 = b^1 \cdot b^1 \cdot b^1 = b^{1+1+1} = b^3 $$, where the dot clearly cannot mean the same as it did in the first example. Here the two dots seem to separate the products of three similar mathematical operations while holding those products distinct from one another within a group.

The question arises, to an uninformed reader, What does the dot mean? Being unenlightened, I would be most sincerely grateful for the explanation. Eebahgum (talk) 23:34, 8 January 2023 (UTC)
 * The meaning of the three dots (ellipsis) is almost the same as in common language; for details, see.
 * The centered dot is a standard notation for multiplication. It is an anomaly that three different notations are used for multiplication in this article. I have added an explanatory footnote for clarification, but the article must be further edited (see the next section). D.Lazard (talk) 10:17, 9 January 2023 (UTC)
 * Thankyou for your response, which I found very helpful. I have added a comment to the thread below. Eebahgum (talk) 18:16, 9 January 2023 (UTC)

Why did this article fall from grace?
In the past, this article was considered as "good" right?

Later, that status has been revoked. How did such happen?

Learning why it happened should be a good idea to help make this article better. - S L A Y T H E - (talk) 17:11, 4 March 2023 (UTC)