people can’t be in two places at once
you also can’t drive it on the roads too much or else the tires will go bad
it’s rough when the math gets so complicated that you have to break your finger in order to be able to visualize things
you could put “AI is making things worse.” after just about any sentence and it would probably be true.
There is also the hilariously misguided belief that good coders do not produce bugs so there’s no need for debugging.
i’m terrified of people who think this way. my experience has been that they are much less inclined to check for bugs in their code and tend to produce much buggier code
i wish they would do this in math instead of the boring system where it’s always alphabetical
that’s an extremely rare sighting but it’s so satisfying to read
what are your thoughts on “whence”?
what’s even the point of a download link if you don’t have a guide that tells you how to click the link
i hope i don’t end up with the -4000 mAh battery if i buy the phone
that would be a lot clearer. i’ve just been burned in the past by notation in analysis.
my two most painful memories are:
there’s the usual “null spaces” instead of “kernel” nonsense. ive also seen lots of analysis books use the → symbol to define functions when they really should have been using the ↦ symbol.
at this point, i wouldn’t put anything past them.
the children yearn for the mines
unless f(x0 ± δ) is some kind of funky shorthand for the set f(x) : x ∈ ℝ, . in that case, the definition would be “correct”.
it’s much more likely that it’s a typo, but analysts have been known to cook up some pretty bizarre notation from time to time, so it’s not totally out of the question.
im not sure if the average republican voter is capable of understanding advanced concepts like “negative numbers”
if you learn how to solve zeno’s problem in the first book, it may be possible to solve 100% of your problems in the second book
i think the ε-δ approach leads to way more cumbersome and long proofs, and it leads to a good amount of separation between the “idea being proved” and the proof itself.
it’s especially rough when you’re chasing around multiple “limit variables” that depend on different things. i still have flashbacks to my second measure theory course where we would spend an entire two hour lecture on one theorem, chasing around ε and η throughout different parts of the proof.
best to nip it in the bud id say
i still feel like this whole ε-δ thing could have been avoided if we had just put more effort into the “infinitesimals” approach, which is a bit more intuitive anyways.
but on the other hand, you need a lot of heavy tools to make infinitesimals work in a rigorous setting, and shortcuts can be nice sometimes
another chicken and egg problem