Talk:Calculus/Infinite Limits/Infinity is not a number

=Seems to be Propaganda?=

Untitled
I don't think I care much for this book. Consider that it, in the introduction, must make an exception for transfinite numbers. How useful is something that has to list out the different types of number-types infinity isn't? In reality, infinity has sort of a dual nature, depending on the use. In the extended real number line, infinity is unarguably an element. Is it a number? I would say yes. In cardinal arithmetic, different sizes of infinity are even used. In the case of limits, the infinity-as-an-unending-process infinity is often used.

I'd say a better name would be "Infinity is not a number in the classical sense" but then we'd have to define what a number is in the classical sense, so I'll go ahead and do that, proposing a new title of "Infinity is not a finite number". That ought to do. Mo Anabre 22:23, 8 November 2007 (UTC)

Merge
This book should become an appendix in the Calculus book.

Useless section
i think that the section "Reinterpret formulas that use $$\infin$$" is useless as it's complicate simple things "i.e. limits". it's enough to say the definition of limit "as x approach something f(x) approaching something else" and let the reader conclude the results with infinity $$\infin$$ as he already know it from the previous sections. That would be easier that rotating around a really simple point. 3D Vector (talk) 18:53, 14 April 2008 (UTC)

Error
The following (unless i'm too tired to realize im wrong) is incorrect:
 * $$\lim_{x \to 0}\frac{1}{x}=\infty$$

However:
 * $$\lim_{x \to 0^+}\frac{1}{x}=\infty$$

and
 * $$\lim_{x \to 0}\frac{1}{x^2}=\infty$$

But:
 * $$\lim_{x \to 0^+}\frac{1}{x}=DNE$$

—The preceding unsigned comment was added by 76.20.246.127 (talk • contribs) 06:49, 26 April 2008.


 * Yes (except for the last where you clearly meant $$x\to 0$$). This was actually fixed by User:Mo Anabre in Nov. 2007 and then un-fixed later. I've re-fixed it. --Mrwojo (talk) 03:08, 18 January 2009 (UTC)

Innacurate page?
I believe this page fails at describing infinity. It can mean two things. The first is the concept on infinity, as in, an unsurpassably high number. That kind of infinity is not a number, since $$\infin$$ + 1 will still be an unsurpassably high number, and, therefore, equals $$\infin$$

The other kind of infinity is that of a number. A number which is the result of R*/0. It is then taken as a number in the Real projective line, and $$\infin$$ + 1 does not equal $$\infin$$ (simply because no number added to 1 equals itself). Remember that, as a number, $$\infin = -\infin$$ Also, calculations such as $$\infin + \infin = \infin$$ are true, just like 0 + 0 = 0.

I would mark this page for innacuracy, but I've no idea of how to do that.

200.158.99.64 (talk) 20:21, 27 May 2008 (UTC)


 * I think the problems with this page exist because it was created for a fairly narrow purpose in Calculus/Infinite Limits, which distinguishes $$-\infin$$ and $$\infin$$ for example. I think a broader, Calculus/Infinity page would be an appropriate step towards making this right. --Mrwojo (talk) 03:37, 18 January 2009 (UTC)

The problem with this article
I believe that the flaw in this article is stating "infinity is not a number". Infinity can both be a number (and therefore infinity + 1 will not equal infinity, which gives it algebraic properties and extinguishes the paradox), and infinity can be a concept. In calculus, you indeed only deal with a tendency to infinity, and that tendency can be both positive or negative. But when dealing with many algebraic conjectures, infinity equals negative infinity (as there is no positive or negative zero), and still retains algebraic property.

My suggestion - merge this into the calculus wikibook. It does not apply to other areas of mathematics.

Just wanted to contribute.

Actually, even in Calculus this is wrong.
The real projective line (one-point compactification) makes infinity a number. The extended real number line (two-point compactification), by contrast, makes infinity and negative infinity into numbers.

The correct statement is really "infinity means exactly what we say it means in this subject, nothing more, nothing less". Or perhaps "infinities aren't like other numbers".

Cantor, etc.
Any student who flatly says "infinity is not a number" based on reading this page will be making a false claim in ignorance of other realms of mathematics outside of introductory calculus. Within the narrow realm being discussed, "infinity is not a number" is admittedly more or less true, but some mention should be made of the larger realm outside of Calculus 101.

Needless to say, mathematicians have defined a variety of infinite cardinals and ordinals, as first analyzed by Cantor. Transfinite values do in fact obey the rules of what constitutes a number; however those rules -- only vaguely alluded to here -- are defined in set theory to accept such values, not reject them out of hand without explaining what those rules actually are, as on this page.

In particular, this quoted section is extremely naive and simplistic, and is arguably wrong, to boot:

'When a list of formal rules applies to a type of object (e.g., "a number") those rules must always apply — no exceptions! What makes different is this: "there is no number greater than infinity".'

This is not only poorly written, but is written in such a way as to communicate "facts" which are not actually true. Anyway, if you claim that all numbers have distinct successors, you must certainly cite a reference for this.

Granting that a page on infinitesimals and infinite limits in the context of introductory calculus needn't discuss these matters in detail, it's probably appropriate to at least mention set theory and Cantor's work on transfinites for interested students.

74.104.144.17 (discuss) 22:32, 14 February 2012 (UTC) Anonymous -- sorry if this doesn't conform to wiki standards, not used to them at all, so feel free to delete or reformat.


 * If infinity includes all numbers then how can you add 1 to it? Where do you get the extra 1 from? All the ones are already inside the original infinity. So it's the difference between reality and symbols that only approximate reality that is causing the confusion. 2603:7000:8240:DA:156D:8255:B332:4A2E (discuss) 04:13, 28 January 2022 (UTC)
 * As human beings we create symbols and definitions of what those symbols mean. If we define infinity as containing all numbers and then write infinity plus one we are simply violating our original definition of what infinity is. 2603:7000:8240:DA:156D:8255:B332:4A2E (discuss) 04:21, 28 January 2022 (UTC)