Talk:Exponentiation/Archive 1

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What is arithmetic?

The present Arithmetic page claims exponentiation as an arithmetic operation. I may be getting it wrong, but I class arithmetic as the art of manipulating numerals - the symbols - in manners isomorphic to the algebraic ops. eg/ie one does not multiply the platonic six hundred seventeen by the platonic nine hundred two, but writes down "617" and "902" and after a bunch of ciphering (the exact word) ends up with another symbol, "556534", representing the number which would come out of the field op on the two inputs. (I'm coming to the point.)

I was taught the four basics plus the extraction of roots (square and cube; I know how it extends to higher degrees but hope never to have to do it). But I've never encountered exponentiation in arithmetic (other than by repeated multiplication, obviously). Is there an actual symbol-manipulation procedure specialised for exponentiation? Please add it if there is one ('cause I'm dying to know what it is). Please change Arithmetic if there is not. 142.177.23.79 23:01, 14 May 2004 (UTC)

Arithmetic is generally understood by people who work with numbers (that I have met) as working with numbers, not numerals. Rules (algorithms) for manipulating symbols are means to help us obtain the correct numbers, but they are just techniques. Different techniques (such as, the use of decimal numerals vs. binary numerals) do not change the facts about the numbers. Thus, facts about numbers are often regarded as legitimate parts of arithmetic even when they do not have symbol-manipulation procedures associated with them. Number theory is often called "higher arithmetic" for this reason. I believe it is fair to say that elementary arithmetic, as in teaching young people how to add and multiply, is heavy on the symbol manipulation, but that is just to learn how to get answers and is not the only part of arithmetic. Zaslav 23:25, 3 February 2006 (UTC)
It is likely possible to manipulate exponents, however you would have to memorize the numbers up to 9^9, though you could disclude stuff like 9^1 if you know 1^9...This is, however, quite difficult.

Exponentiation or Involution??

Go to Talk:Super-exponentiation. It says there that exponentiation is properly called involution and that exponentiation is just an awkward term. Any votes to move this page?? 66.245.22.210 17:46, 3 Aug 2004 (UTC)

Our heroes at Encyclopedia Britannica use the balanced terms "involution" & "evolution" as the standard to refer to the 3rd binary operation and its inverse. ----OmegaMan

Every mathematician I know (and I am one and know many) calls this operation "exponentiation". Not one of them ever said "involution" in my hearing, or in writing that I read. Zaslav 23:13, 3 February 2006 (UTC)

"Extracting a root used to be called evolution." This is as uncommon as calling exponentiation for Involution. The article on Evolution does not mention that meaning of the word. I will delete the sentence. Bo Jacoby 10:57, 24 May 2006 (UTC)

I think this article needs a History section; obsolete terminology (with citation) might be appropriate there.--agr 11:35, 24 May 2006 (UTC)

(x+h)^3

Where can I find the page that tells how to cube two variables that are being added or subtracted? I can't find it anywhere... pie4all88 22:48, 26 Sep 2004 (UTC)

Try binomial theorem. Revolver 04:00, 27 Sep 2004 (UTC)

1

Exponentiation in abstract algebra

The stuff about power-associative magmas in the abstract algebra section of the article is wrong. Power associativity is not enough to get this sort of thing to work, as the following 3-element magma shows:

   | 1 a b
 --+-------
  1| 1 a b
  a| a a 1 
  b| b 1 b

The above magma is power-associative, it has an identity element, and every element has a unique inverse. Yet a2a-1 is not equal to a.

I'm going to change the article to use groups instead. It's possible to do it in somewhat greater generality than that (e.g., Bol loops), but it's probably not worth it. --Zundark 19:58, 17 Dec 2004 (UTC)

An excellent idea. Generality can be excessive. Zaslav 23:15, 3 February 2006 (UTC)

Decimals

This article doesn't say anthing about powers with non-integer exponents (i.e. decimals, fractions, etc.) I don't know much about it, so could somebody put it up? →[evin290]

merging

It has been suggested that this article or section be merged with exponential function.

I think this is a bad idea. The (real of complex) exponential function is just one aspect of exponentiation in general, and the variety of topics in the article suggests this. Revolver 20:48, 14 August 2005 (UTC)

I am a high schooler, with not so good math skills. This article is very helpful for studying and basic learning about the math that I have trouble with. Making this merge with another would only make it more complictaed for me. Please keep them seperate so I can get the basics down. -Thanks Bigfoot

"powers of one"

This § does not in fact appear to be about powers of one. Can anybody propose a more sensible title for it? Doops | talk 23:19, 9 November 2005 (UTC)

Hi Doops. I wrote it and used the notation 1x meaning e2πix, because e2πi = 1. However, this nice and useful notation was deleted by other wikipedians who considered it 'original research'. Only the title survived. Bo Jacoby 15:31, 11 November 2005 (UTC)