bryn
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 Nov3 comment Explanation of method for showing that 0 / 0 is undefined I see that this comment was made four years ago, but I said that I would revise or defend my position on the basis of comments. So, could a simple example be provided of one particular part of mathematics that would be broken as a result? Oct20 comment Why must the base of a logarithm be a positive real number not equal to 1? This doesn't answer the question about why the base of the logarithm cannot be negative. Oct8 comment If all vectors in a set are perpendicular to a given vector, is the set linearly dependent? Hmmm, I should have specified that I was considering three vectors over three dimensions, or two vectors over two dimensions. Not sure whether I should edit the question or pose a new one. (Although my reason for suspecting it to be true is now looking dubious, so perhaps I should just ask for a counterexample to the conjecture.) Jan8 comment What's the explanation for why n^2+1 is never divisible by 3? I like the first three paragraphs, although I'd start the first with "For any integer $n$,". Why not conclude with "Thus, for any value of $n$, either $n^2$ or $n^2 - 1$ is a multiple of three, so the next multiple of three above $n^2$ is either $n^2+2$ or $n^2+3$."? Dec12 comment Are there any interesting semigroups that aren't monoids? Although this answers the question in the title, it seems to ignore the second paragraph where I try to tighten what is meant by the question. Dec1 comment Why is the volume of a cone one third of the volume of a cylinder? Yes, it's not clear what the "so forth" means -- what is the fourth dimensional counterpart? Nov16 comment Functions over $R$ such that $f(xy) = f(x)f(y)$ Oh yes, I forgot all about the fact that $(xy)^n = x^n y^n$. So I guess the answer to the first question is "yes", but my second question remains. May5 comment Optimal Strategy for Deal or No Deal Thanks Zev for fixing up the $signs. How do you get them to not make it go into LaTeX mode? Aug15 comment Is there a name for$[0,1]$? I'd imagine the 'unit interval' refers to the set [0,1], but you wouldn't say that the number 0.3 is a "unit interval number" in the same way that you might say that 2/3 is a "rational number". It's not entirely clear from the question but I think it's asking for a term to describe any number in the set, not to describe the set itself. Aug12 comment Interesting properties of ternary relations? Okay. That is interesting but it's not the type of property that I was after -- I want properties expressible in first order logic (+ identity). Aug7 comment Interesting properties of ternary relations? I'd be interested to hear some of those properties. The only one I can think of (off the top of my head) is R(x,y,z) <-> R(y,x,z). Aug3 comment Interesting properties of ternary relations? I'm now sure why you put that as a comment rather than as an answer. Aug3 comment How do the Properties of Relations work? Asymmetric does not mean "not symmetric" in the context of binary relations. The relation "x is a factor of y" is not symmetric (since 3 is a factor of 6 and not vice versa). But it is not asymmetric either by any standard definition of asymmetry. Jul29 comment Characterising functions$f$that can be written as$f = g \circ g$? @Qiaochu -- thanks for finding that for me. Could you put it as an answer to the question, optionally with a brief summary? Jul29 comment Characterising functions$f$that can be written as$f = g \circ g$? Thanks - fixed it. Jul29 comment Group with an endomorphism that is “almost” abelian is abelian @Mariano, why don't you give that as the answer and then it can be accepted? Otherwise it looks as though nobody has answered the question. Jul28 comment Why is the “finitely many” quantifier not definable in First Order Logic? Yes, I agree that the fact that I could define$P_3$was irrelevant because of the inability to form an infinite disjunction, but I included it to give the question a bit of a context. Jul28 comment If$A$is a subobject of$B$, and$B$a subobject of$A\$, are they isomorphic? I don't know the answer to your question but being antisymmetric is stronger than what you have here. If 'being a subject of' is antisymmetric then A and B should not just be isomorphic but identical. Jul28 comment How do the Properties of Relations work? @Charles: (Deleted old comment too). To tell you the truth, I felt as though the question didn't make much sense -- it was more like "please explain the entire theory of relations including all relevant distinctions". So I thought I'd at least define the terms properly. Jul27 comment Why is the derivative of a circle's area its perimeter (and similarly for spheres)? I hadn't thought of this. Does this also explain why it works in 3 dimensions?