On Date: Sun, 6 Jan 2013 13:39:57 -0600, Paul Brandon wrote:
Your final quote was the sense I'm familiar with; the term 'infinitely
positive or negative ....' uses the term as a modifier, not a noun.
See: http://scienceblogs.com/goodmath/2008/10/13/infinity-is-not-a-number/
Just a couple of points:
(1) What is the antipode of a Riemann sphere?
HINT: If you read the comment by Sigrpe on the blog addressed
above, then you'll see:
|Speaking as someone whose blog is named after the antipode
|of zero in the Riemann sphere I really have to differ with this article.
|There are perfectly sensible rules for working with the infinity on
|the Riemann sphere. We can add, subtract, multiply and divide
|by infinity, as well as define functions that are continuous and
|differentiable at infinity. In fact, moving from the complex plane
|to the Riemann sphere can make many functions much better
|behaved, and that's why people do it.
|
|I can see arguments for not calling this infinity a number. But the
|argument that it's not a number because it breaks some rules is
|very unconvincing, after all the negative numbers and complex
|numbers also break many rules that some people would say were
|essential properties of numbers.
|
|Ultimately you draw the line between numbers and non-numbers
|using taste and utility.
(2) If you really, really, really believe that infinity cannot be a
number, then shouldn't you be busy pointing this out to the articles
that I linked to in previous posts that appear to make this claim
that it can be used as a number?
I suggest you start with Wikipedia and try to change the entry
on "Negative temperature" where this is most obvious. Consider
if there is a discontinuous jump from positive infinity Kelvin to
negative infinity Kelvin, what value of positive infinity is involved
if it is boundless or "beyond limit"?
-Mike Palij
New York University
[email protected]
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