@robjohn I think the monolith comparison fits the subject of Algebra because it is so massive and can be viewed from so many different perspectives, what do you think Rob?
While analysis, as you mentioned, is more abstract like psychology.
@Skullpatrol Analysis in math and analysis in psychology are very different. Level of abstraction varies heavily within both algebra and analysis. Abstraction in analysis is made easier with the help of algebra.
@JonasMeyer Psychology has intimate ties to Philosophy and so the level of abstraction gets pretty high pretty fast ... but as you said Analysis is made easier with Algebra.
If you tell someone you work in algebra, you get typical responses like "Oh, I was never very good at algebra." If you tell someone you work in analysis (and the person has little math background) they might assume a different meaning. My aunt's response was, "Oh, yeah, I've worked a lot in analysis, too."
@JM Exactly. I knew some students who worked more or less in analysis but said they always used more specialized descriptions if asked by friends/family to avoid (?) misunderstanding.
@Skullpatrol I am not sure I particularly care either way. I meant the exclamation mark as a danger or alarm signal, but the question mark has a compelling case too.
@leo You should do something similar for the other way round as well. Let me think.
OK, let's try to prove $LHS \leq RHS + \varepsilon$ for every $\varepsilon > 0$. That will show $LHS = RHS$. I am not sure if this is the optimum route. :-/
@robjohn I once tried to hunt down the origin of "the question mark over the equals sign" as an abbreviation for "Is this statement true?" But found no meaningful results. Have you ever seen anything on it?
I know you did; I wasn’t accusing you of contempt. I’m just not particularly comfortable with it. I didn’t really mind, hence the smiley, but it’s definitely not necessary. I didn’t mean to make you feel bad.
@anon With the way some people dress today, I've found it easy to make mistakes...
@Srivatsan Curiosity, more than anything. Also I've seen at least one site where there was a father and son both registered and answering on an SE site, but I no longer recall the example.
@Srivatsan, fix $(a,b)\in A\times B$. Then $\inf_{v\in B}f(a,v)\leq f(a,b)$, and then $\inf_{u\in A}\inf_{v\in B}f(u,v)\leq f(a,b)$, and then we are done. Are you kidding me?
There was this guy that asked three questions about cardinals and AC; in the comments he told me that he is an applied mathematician and doesn't know much about those things; online he ran into someone claiming you can prove CH if you limit multiplication by zero to finite cardinals only.
Then, a few days later, comes another guy asking about definition of cardinal multiplication and does multiplication by zero remain defined without the axiom of choice.
@Skullpatrol I doubt that it comes from anywhere in particular: it’s a very obvious thing to do. I’m pretty sure that I ‘invented’ it independently at some point.
This Aurifeuillian factorization of cyclotomic polynomials that Dubuque mentioned in an answer is just so cool I'm going to have to link it here. It makes me want to get a blog just so I can link to these things.
In the first I passed, but failed the sober resit (I figured I could get a higher grade if I'm sober); in the second I failed but it was a good thing. The resit was so much easier that I got 92.
@BrianMScott I think I was confused about defining $G^\ast$ the other day because towards the bottom of the page they define it in terms of $F$, or at least that's what it looks like to me.
(I finished dancing already.)
@AsafKaragila I don't get it. If you passed why would you have to re-sit?
(Took a while for the page to load.) No, $G^*$ is given. The theorem then says that there is a function $F:\omega\to X$ that has a certain relationship to this given $G^*$.
The following year I'd taken measure theory as well, and although I got 84 in the exam of measure theory, in the retaken exam I barely scraped 57 again. This time I did not try to resit.
