desacsndioa

"whenever" made more sense to me than "by requiring", the latter still confuses me.

Thanks, I think I understand it better after looking at the definition for limits as x approaches infinity: f(x) gets arbitrarily close to L whenever x is sufficiently large. I was thinking of x as a specific value, rather than a range.

The actual definition is: For every ε > 0, there exists δ > 0 such that for all x, if 0 < |x - a| < δ then |f(x) - L| < ε, but I don't get how the formal worded definition means this. Been staring at it for probably 2 hours now.

As in the function above, it can get arbitrarily close to 3 since we can to go from the left and right side of x = 7. As in x = 6.999 and 7.0001, which might be sufficiently close to a = 0 depending on what is defined as arbitrarily close.

I'm trying to understand the formal definition of the limit, but it seems that if you can define "sufficiently close" as whatever value, then you could say that a limit exists when it actually doesn't.

Since I am saying a = 0.

Yea, but then based on that definition, we can say a limit exists at 0, when it doesn't.

Then x would be close to 7, and |x - 0| = |7 - 0| < 10, which might be sufficiently close?

For example, there might be a graph of f(x) = {2 x<=0, 4 0<x<=4, (x-4) x>4} and and f(x) will get arbitrarily close to 3 if you define sufficiently close as 10.

It's the formal definition of a limit I found in a few texts, but it seems to work on things that aren't actually limits, since it depends on what you define as sufficiently close.

Lol, I am learning some graph stuff and decided to visualize MathSE tags by similarity.

The number being divided (a) is being varied across a range, when it reaches the end of the range it reverses. The full size versions are f3 and f4. The horizontal lines are actually meant to be points on the right side of them, which represent the remainder as a divides by x.

@UmbQbify-Key20- Lol, I think it looks cooler backwards though.

Made a funny visualization of factors: desmos.com/calculator/0ssikt8mo7

@ROODAY It depends what axis you want to flip the coordinates over, doesn't it? But you would translate all the points, such that the corner becomes (0, 0), perform the reflection, then translate everything back.

Just "Calculus" @psa

I think I'll just plough through Spivak's Calculus and it might polish those areas along the way :P

I have a linear algebra textbook I tried for a while, but it covers equation solving mostly, and other linear algebra "stuff" (maps, determinants, similarity, vector spaces). I'm mainly trying to learn calculus now (based on an SE textbook recommendation) and polish the areas above.

Thank you. Conics, loci and complex numbers are scattered throughout my textbook (a general textbook for the maths course at my HS), but the problem is that it wasn't quite in depth, and I'm not sure what textbooks to use now for self study. There were higher order root solving, but these were quite "rigged" (we're usually given a solution, told to find the others). Is there an all encompassing area of maths to describe these topics?

Sorry, clicked enter on iPad prematurely.

Just a soft question, are conic sections (, complex numbers, quarternions considered "elementary" algebra? I'm looking for a book recommendation question

Seems like the drivers are up to date. Don't have modifications to the taskbar. Wish I remembered whether I tried restarting explorer.exe. I don't really know what info to log if it happens again. Wifi seems really dependent on ms-settings though; for example there is no way to use wifi from cmd if it is not physically toggled in ms-settings.

1903, it just updated today for a security update.

Thanks. I'm not sure how to trace the problem. There's a question on Microsoft Answers with 8500 upvotes yet no accepted solution. I should have wrote down what I tried; it happens at the most unexpected times, not sure how to invoke the bug.

Anyone have this issue in Win10: Occasionally the system (Settings, control panel, Wi-fi, start menu, Windows 10 default apps) seems to die. Largest issue is that Wi-fi is inherently connected to this Windows 10 "interface"; even if you re-enable it via cmd, it doesn't work. Characteristic symptom is that Wifi-discovery menu shows no networks at all (even though netsh does), no wifi-button (?). Seems a bit of an open-ended question but has lots of similar questions on Microsoft Answers.

Michael, thank you for your insight. I also noticed that based on those functions, the recursive ones seem to use a pattern approach. Also, cool Christmas tree!

Just two things I've been wondering about.

Also, why does Position[{a, {a, b}}, x_ /; Print[x], 1] output List, a, {a,b} while Count[{a, {a, b}}, x_ /; Print[x], 1] outputs a, {a,b}?

Is there a logical reason why some functions such as Select, GatherBy, SplitBy use functions as a "test" whereas some other functions such as Count, Position uses patterns as the "test"?

@anhnha Interesting, Geogebra is able to plot the equation. One way of doing it might be to just plot the parametric function {t, t, t}, which should be equivalent. Or the intersection between planes y==z&&x==z. I'm sure there's a better way of doing this though.

The arguments of Apply will get evaluated first, where {Sequence[{a, b, c}, {d, e}]} -> {{a, b, c}, {d, e}}

Since it's basically Apply[f, {Sequence[{a, b, c}, {d, e}]}, {1}]

I think it's because the sequence gets converted before @@@ is applied.

a, b, c isn't a sequence but a List in {{a, b, c...

Oh, why would should it be considered a sequence?

@anhnha What you are after is @@. which replaces the Head (which is List). @@@ applies @@ to each of the elements, and is equivalent to f @@#&/@ {{a,b...

I like Mathematica so much, it has almost everything, it's just crazy. Soz, just had to say it.

Thanks! I wouldn't have caught that. For some reason clicking on the + button does not seem to work, it stopped working a while ago.

I'm not sure if I missed something trivial. Why is the cell highlighted in red even though there are no errors, and everything is working as expected? This has happened a few times.

Thanks for the tip! This will definitely come in handy.

Running Accumulate[] on a list with quantities takes a long time (never finished because I aborted), whereas running Accumulate[QuantityArray[list_of_quantities]] is almost instantaneous.

I wonder why it takes so long to run Accumulate[] on a normal list, when it is almost instantaneous for a QuantityArray[] (generated by GeoDistanceList[]).

Yes, luckily Mathematica has a built-in function for that. The max separation between points is below 200 metres (rare event where gps link lost), so I think the error is acceptable.

Ah yes, that would do just fine. Thank you.

Is there some default function in Mathematica that will allow me to calculate distances between two geographic points (lat, lon), each with an associated elevation? GeoDistance does not take into account elevation changes. I'm working with GPX files, which have been parsed neatly using the inbuilt functions.