Mike-- I'm not a mathematician; neither are most physicists. We use tools that appear to work for us, whether they are technically correct or not. For instance, when I did my dissertation on counting behavior by rats, I considered using signal detection theory and rejected it because of unmet assumptions about my data. Ten years later, an editor suggested that I apply an ROC analysis to my data. I did so, the results appeared orderly and tied together a number of sets of observations, so we concluded it was justified.
If I really wanted to know whether mathematically infinity can be treated as a number, I'd ask my son the maths professor specializing in number theory (I may do that when he gets his latest batch of grades in, something I don't have to worry about any more). On Jan 7, 2013, at 8:11 AM, Mike Palij wrote: > 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"? Paul Brandon Emeritus Professor of Psychology Minnesota State University, Mankato [email protected] --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=22726 or send a blank email to leave-22726-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
