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I teach physics at Fullerton College, a community college in Southern California.


14h
comment Best applications-oriented introductory calculus textbooks?
Agnew may actually be public domain now. Its copyright was in 1962, and it doesn't appear to have been renewed.
Jul
2
awarded  Curious
Jun
24
comment Standard terminology for infinite limits with opposite sign on the two sides?
Well, the former limit doesn't exist, and the latter does (it's +∞). I'm sure what else there is to it. As stated in the question, I don't think that's standard terminology. I think standard terminology is that neither limit exists.
Jun
24
revised Standard terminology for infinite limits with opposite sign on the two sides?
added 265 characters in body
Jun
24
comment Standard terminology for infinite limits with opposite sign on the two sides?
Thanks, but I'm not asking how to verbally describe the left and right limits. I'm asking how to verbally describe the distinction between the two cases demonstrated by $1/x$ and $1/x^2$.
Jun
24
comment Standard terminology for infinite limits with opposite sign on the two sides?
@Omnomnomnom: I should have specified: it is sometimes the case that it would be considered wrong to say that the first limit does not exist OK, if the terminology is not totally standardized then that would be good to know. However, in the small sample of books I have handy on paper or online, all seem to define the first limit as not existing.
Jun
23
comment Standard terminology for infinite limits with opposite sign on the two sides?
@mm-aops: So how would you distinguish the two cases in the question? #1 "has an infinite limit," while #2 "has no finite or infinite limit?"
Jun
23
comment Standard terminology for infinite limits with opposite sign on the two sides?
We talk about "lateral limits". The limit with "+" is the limit from the right, and the other is the limit from the left. Yes, I understand that. One could certainly describe them as "a limit that is infinite and has the same sign from both sides" versus "a limit that is infinite and has opposite signs from the two sides." However, that would be very cumbersome.
Jun
23
comment Standard terminology for infinite limits with opposite sign on the two sides?
@TomCruise: Are you saying you'd describe the second limit as existing but not converging? AFAICT from looking at various sources, that would be nonstandard.
Jun
23
comment Standard terminology for infinite limits with opposite sign on the two sides?
@Omnomnomnom: As far as I can tell by looking at various sources, people describe both of these limits verbally as not existing. I'm asking for a verbalism that distinguishes the two cases.
Jun
23
comment Standard terminology for infinite limits with opposite sign on the two sides?
Thanks for your answer, but I understand how to notate it. I'm asking for verbal terminology.
Jun
23
asked Standard terminology for infinite limits with opposite sign on the two sides?
Jun
15
awarded  Tumbleweed
Jun
8
revised Generating possible/impossible pairs of functions to integrate
deleted 24 characters in body
Jun
8
asked Generating possible/impossible pairs of functions to integrate
Jun
2
awarded  Nice Answer
May
29
awarded  Pundit
May
25
accepted Least pathological case where limit of middle Riemann sum with uniform partition $\ne$ Riemann integral?
May
21
comment Least pathological case where limit of middle Riemann sum with uniform partition $\ne$ Riemann integral?
If you feel like expanding this into an answer, I'd like to accept it. I'm not completely clear on what it means for a function to have countably many discontinuities. The function I described in the question is discontinuous at uncountably many points, but can be made continuous by removing countably many points.
May
21
comment Least pathological case where limit of middle Riemann sum with uniform partition $\ne$ Riemann integral?
@AndresCaicedo: OK, but that's also highly discontinuous.