Nathan
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 Nov 2 comment Directions to the Algebra Zoo? The latter, yes. Oct 30 comment Alternative Arithmetics If there examples of truly novel arithmetic, I'd be really excited to hear about them. This game is really, really limited, and admittedly not exciting. Are there other things that are exciting? Oct 30 comment Alternative Arithmetics I think you're getting stuck on aspects of the question I don't really care about. I'm not claiming that this is an unprecedented mathematical system totally new in mathematics, or that there's no way to reduce it to pre-existing systems. Just that, for the people who were learning the system, it was something they hadn't seen before. Oct 30 comment Alternative Arithmetics Yeah, it's pretty simple, and it's really easy to come up with a different way to think about it. But the point is that it's an example of the kind of 'novel arithmetic' I'm curious about. Sep 28 comment Under what conditions does matrix multiplication commute? @IvanNeretin Oh ok. I see where I messed up then. Thanks! I didn't know about \limit. I've always just written it the other way. Sep 28 comment Under what conditions does matrix multiplication commute? @user1551 Hm. The summation is supposed to capture that each entry is the inner product of a row of A and a column of B (or the other way around). Oct 31 comment Probability (X >Y) when X and Y have the same distribution? "Let Y be the next day after X" - i.e. Y = X + 1 (mod 7). The only way that X + 1 > Y is if X = 7. Basically, you're reasoning isn't wrong, it's just that you misread the question. I do this all the time. Aug 1 comment Confused by definition of an open set in “All the Mathematics You Missed” That's what I thought, but I am not nearly confident enough of a reader to say "that's wrong". Thanks. Feb 15 comment Proof that $\int_1^x \frac{1}{t} dt$ is $\ln(x)$ @BrianM.Scott Yeah, sorry. I looked through and I couldn't find it, but once gingerjin gave a proof I recognized it. I was too impatient, is all. Thanks anyways! Feb 15 comment Proof that $\int_1^x \frac{1}{t} dt$ is $\ln(x)$ Thank you. This is a really clear explanation! Feb 15 comment Proof that $\int_1^x \frac{1}{t} dt$ is $\ln(x)$ @JonasMeyer I'll see if I can find something about $e^u$. Maybe that will help me understand this. Feb 15 comment Proof that $\int_1^x \frac{1}{t} dt$ is $\ln(x)$ @HenningMakholm Apostol's "One Variable Calculus". If there is a proof, I'm missing it. Nov 29 comment Limit of $1/x^2$ - Apostol 3.2, Example 4 Oh! I think I get it. Any neighborhood N(0) will contain points such that 0 A+2. You can't get around that, no matter what δ you choose. What makes me sure that I get it is that now I don't understand why I didn't see that in the first place. Nov 29 comment Limit of $1/x^2$ - Apostol 3.2, Example 4 On reflection, I'm not sure either. This is helping, though. Thanks! Nov 29 comment Limit of $1/x^2$ - Apostol 3.2, Example 4 Thanks for the formatting. I briefly tried to get it into LaTex, but I gave up after nothing worked. Haha. I've tried to ask questions where I didn't explain as much, and the person I was asking either refused to help or started talking about a part of the problem that I wasn't asking about. In this case, I had already burned through all of my mathy friends, but they are all at least two years out from real analysis, and couldn't help very much. They did help me get this far, though. Nov 29 comment Limit of $1/x^2$ - Apostol 3.2, Example 4 I think I get it. Is this like saying that for a given δ1 such that for 0 < x < δ1, if δ1 does not work, than no δ > δ1 will work?