Talk:Abuse of notation

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[edit] Screwdriver?

I am not sure what you are trying to do with this page, in particular the opening comment is almost content-free. I always use screwdrivers to open paint tins. 8-) (and no, this is not vacuously true - I've been painting my house recently). I would think a page on abuse of notation should also describe why it is a useful thing to do, as well as describing why the examples are actual abuses of notation. (e.g. always insisting that functions and variables have distinct symbols leads to proliferation of symbols that only the most anal retentive mathematician (or painter) would delight in.) Andrew Kepert 01:45, 6 Apr 2005 (UTC)

Hi Andrew, Sounds like you could have made a better start at this than me. I used an abuse of notation recently in Combinadic so thought there should be such a page, but am still at a loss what should go into it. --J. W. McLeod 09:28, 6 Apr 2005 (UTC)

[edit] Very common abuse?

"A very common abuse of notation is using sin2(x) instead of (sin(x))2."

It's not an abuse at all according to other things I've read - fn(x) = [f(x)]n for n not equal to -1 (for n=-1 it refers to the inverse function). The article Function (mathematics) seems to make no reference to this. Brianjd | Why restrict HTML? | 04:56, 2005 Apr 8 (UTC)

+ Especially in the abstract, fn(x) = f[f(x)] However, sin2(x) is an exception to the rule. Bluap 16:48, 3 May 2005 (UTC)

[edit] Have retreated from language criticized above

The present version would seem to make a better stub for this topic. I don't think there is much of a controversial nature left, but there remains enough structure so that it's pretty clear what the intended topic is. --J. W. McLeod 12:48, 10 Apr 2005 (UTC)

[edit] John Harrison

Who is John Harrison? --Abdull 08:29, 30 May 2006 (UTC)

[edit] Infinite limits

I don't think \lim_{x \to \infty}f(x) = \infty qualifies as abuse of notation.

  • If the domain and codomain under consideration are the extended real line, the limit may very well exist, and have the precise value of \infty, without any notational or conceptual difficulties whatsoever.
  • If the domain and codomain under consideration are \mathbb{R}, then, as described, the limit does not exist (edit: and neither does the infinity), and, therefore, the sentence is not false but meaningless when considered merely as the sum of its parts, so the idiom (essentially bringing the extended real line into a real context) gives meaning to an otherwise meaningless sentence, rather than giving an additional meaning to a meaningful one.

Dfeuer 04:36, 30 October 2007 (UTC)

Yes, \lim_{x \to \infty}f(x) = \infty has a precisely defined meaning, as our own article on limits shows. I'm getting rid of that example. -- 75.162.71.236 04:15, 8 November 2007 (UTC)