these are not arguments. they are beliefs/opinions

it’s rough when the math gets so complicated that you have to break your finger in order to be able to visualize things

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

could not be me in the second frame

libertarians are conservatives with even worse critical thinking skills.

most conservative arguments fall apart when you ask 3 consecutive questions, but it only takes 1 or 2 questions for the typical libertarian argument

“accidentally”

i wish they would do this in math instead of the boring system where it’s always alphabetical

not if you line things up right

how do you know

that’s an extremely rare sighting but it’s so satisfying to read

what are your thoughts on “whence”?

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:

• in the (baby) rudin textbook, he uses f(x+) to denote the limit of _f _from the right, and f(x-) to denote the limit of f from the left.
• in friedman analysis textbook, he writes the direct sum of vector spaces as M + N instead of using the standard notation M ⊕ N. to make matters worse, he uses M ⊕ N to mean M is orthogonal to N.

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

what happened to that guys sleeves

unless f(x₀ ± δ) is some kind of funky shorthand for the set f(x) : x ∈ ℝ, x - x₀ | < δ . 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.

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

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