I suspect that's because us rookies are drawn to maths given that it promises complete precision, and then you see that you have to go down, down, down... to actually realize that promise. I am content for now going no further than Enderton though
it's not the end of the world to power through anything, and i don't want to make it out like it's scary or inaccessible, i just wonder whether everyone bothers to examine why they want to do set theory
it's like if you were learning a language, at some point in acquiring the rules of grammar, and their big exceptions, and the histories of how words or figures of speech developed from other words or languages, eventually you reach a point where you're learning stuff that > 99.9% of native speakers have never heard of and never use
and with something like set theory, you hit that point sooner than a lot of people think
and yeah i actually wonder how many books are actually worth reading start to finish
a lot of standard textbook advice fits the format "read through chapter x and then stop," where x is often only a little more than halfway through
But surely something to be said for just enjoying a good book :) I agree some are slogs, but some are just really pleasant. (Baby) Rudin fell in the first category (at least for me), but Enderton I am really enjoying. LADR was another beautiful one
LADR was long ago and I'm so out of practice that i gotta do another LA book sadly, hence hoffman and kunze
i believe that some people might have hit chapter 8, because i did, despite xander's advice (which is the best advice and the advice taken by my first analysis prof). but nobody has ever gone through chapters 9, 10, and 11 of rudin. you can't. your brain shuts off.
@Jakobian suppose if there is a sinx term in an expression and the x tends to zero, they multiply and divide by x and take that particular term to be 1
@KavinIshwaran you can't do that unless it makes sense with respect to the rules that limits obey e.g. products, sums, quotients of limits
You would have to be more specific and only then we can discuss if in a given limit it makes sense to make such substitution. In general the answer is no, it doesn't make sense
to be more specific, in a question which goes like this : limit x tends to zero (tanx - xsinx)/x they multiplied sin x by x and divided it with x (that particular term alone and then LH rule is used)
@Jakobian Oh Ok. I will make a memory note on this.
The above is supposed to be an example of a sequence that converges in mean but not pointwise a.e. I simply do not understand it, since I believe there are some typos. How can n increase from $2^m$ to $2^m-1$? Also, is $f_4$ correct? Mightily confused.
Trying to figure out what the correct example should be...
The typewriter sequence is an example of a sequence which converges to zero in measure but does not converge to zero a.e.
Could someone explain why it does not converge to zero a.e.?
$f_n(x) = \mathbb 1_{\left[\frac{n-2^k}{2^k}, \frac{n-2^k+1}{2^k}\right]} \text{, where } 2^k \leqslant n < 2^{k+...
