Talk:Exponentiation/Archive 2016

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Multiple exponents in a series

Arecent edit replaced "Exponentiation alone is not commutative" with this:

"Exponentiation alone is not commutative but multiple exponents (often termed factors) are when they are used in a commutative group such as in Multiplicative group of integers modulo n or Diffie–Hellman key exchange."

I think this is misleading. Non-commutativity of exponentiation is $a^{b}\not =b^{a}$. It's rarely true that one would have equality here, and being in a "commutative group" (whatever that means) doesn't help. I am assuming what is intended here is that $(a^{b})^{c}=(a^{c})^{b}$, which follows from commutativity of multiplication and the fact that $(a^{b})^{c}=a^{bc}$. I don't know if this point is worth belaboring though. However, it is difficult to see what this "commutative group" is. This is true for positive integer exponents (for example), but those don't form a group. In the example given, the exponents are just boring old integers. Sławomir
Biały 22:38, 1 January 2016 (UTC)

Promotion of notational-history section

In a recent edit, User:Dan6233 moved the "history of notation" section up to the first section after the lead.

My first reaction was that this puts too much weight on notation. Notation is much much much much less important than the math. Radically less important. Exponentially less important.

However, when I look at the article as it currently stands, I don't find it too objectionable. It's a reasonably short section, and it is traditional to deal with history near the top. As long as it doesn't grow, it seems sort of reasonable. But I'm concerned that it might grow.

Here's my thought, not really fleshed out: What if we turned it into a history section, rather than history of notation specifically? We could treat the history of the concept and of the notations sort of in parallel. If done well, that might yield a section that could grow sort of organically, without overemphasizing notation.

Thoughts? --Trovatore (talk) 00:00, 23 September 2015 (UTC)

All sounds reasonable to me. I agree with it being of less importance for the people coming here but we can afford to order to some degree by largest importance/size first. Just naming it History sounds good and leaves a bit of room for expansion. Dmcq (talk) 14:10, 23 September 2015 (UTC)

I am not a mathematician , and I found the history of notation very helpful. Thanks for keeping it up front.

May I suggest that after the sentence "Thus they would write polynomials, for example, as ax + bxx + cx3 + d," you provide in parens the modern notation for polynomial equations? That would allow the nonexpert reader, who does not have that information handy in the local memory bank, to see the difference between the two. The sentence would read, "Thus they would write . . . (instead of . . . , the accepted notation today).

Thanks. KC 16:50, 29 February 2016 (UTC) — Preceding unsigned comment added by Boydstra (talk • contribs)

iⁱ

At the bottom of the section named Computing complex powers, there is a sentence that says: "[...] there is an infinity of values which are possible candidates for the value of iⁱ, one for each integer k". I would like to be clarified on this: does that include negative integers, too? Mvpo666 (talk) 22:10, 15 September 2016 (UTC)

Yes. Dmcq (talk) 23:33, 15 September 2016 (UTC)