What would YOU call this?  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: What would YOU call this? (/thread104520.html) 
What would YOU call this?  Chuck  12222006 Last week a few friends and I discussed this "function":
p.s. Stay out of the complex's. :)
Re: What would YOU call this?  Valentin Albillo  12222006 Hi, Chuck: I guess you want this:
f(x) = ln(1x)+ln(x2)
Best regards from V.
Re: What would YOU call this?  Chuck  12222006 Ahh, but your first step is not allowed; you have drastically changed the function. The original function f(x) = ln(1x)+ln(x2) Re: What would YOU call this?  John Gustaf Stebbins  12222006 Looking at a couple definitions of "function" I guess you could say that it is a function on the empty set, assuming you consider the empty set to be a valid domain. Doesn't seem proper, but I don't see where the laws of mathematics would fall apart.
Re: What would YOU call this?  Crawl  12232006 I'd call it a function, because "stay out of the complex" is an artifical human requirement, while analytic continuity is mathematically natural. I'd also say x / x = 1 at x = 0 (not that it's undefined), and 1  1 + 1  1 + 1 ... = 1/2, though. If you want to have a function that has no domain, why not define a function that really has no domain? Or at least something weirder than the logarithm, which is a perfectly normal function, except that it's multivalued. How about f(x) = 1^x + 1^(2*x) + 1^(3*x) + 1^(4*x) + 1^(5*x) + ... which diverges to infinity for all x. Or even use something nonmathematical.
f(x) could take values, but since it's hard to establish if one number loves another, it might be undefined for all x.
