unless f(x~0~ ± δ) is some kind of funky shorthand for the set { f(x) : x ∈ ℝ, | x - x~0~ | < 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.
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
don’t you dare
that’s the spirit
real men don’t have time to waste peeling bananas. you either smash it on your forehead and eat the nutrients as they slide down, or you eat the whole thing in one bite.
the rest of the chocolate chips are sleeper raisins. one click of a button and it’s an oatmeal raisin world.
seen and not seen in my ass
what happened to that guys sleeves