Jack M
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 Mar7 comment You need to buy 100 birds for $100? how to find answer.. This problem can be solved using the same method I used on this question, but you probably haven't covered congruences yet. Mar7 comment How to prove the relation is transitive? @committedandroider You would probably want to prove that the sum of two numbers is even iff the numbers are the same parity (which would end up being as long as proving transitivity directly), but it has the advantage of making it clearer why the relation is transitive. Mar7 answered How to prove the relation is transitive? Mar6 comment What is a symmetric polynomial? @mercio It connects to what I said about point (2) in my question - it's not so much that I don't understand the definition as that I don't like it. Is there no more elegant definition? Mar6 comment What is a symmetric polynomial? @mercio I've seen$K[x]$defined as a sequence of coefficients, I suppose, but that always struck me as an ugly definition. Mar6 asked What is a symmetric polynomial? Mar4 comment Are there many fewer rational numbers than reals? @YvesDaoust That's not an argument, it's a vague intuition. What your critics are saying is that they disagree that that intuition is convincing. Mar3 asked False proof that$F_{3^2}$contains$F_{3^4}$Mar2 comment If$ad - bc = 0$, then$\begin{cases} ax + by = j \\ cx + dy = k \end{cases}$has no unique solutions @Reveillark Given the OP's level, that's very much begging the question... Mar2 comment Showing a Set is Unbounded Given a Continuous, Unbounded Function Choosing a function at all immediately invalidates the proof - you're meant to prove that the statement is true no matter what$f$is. It would be a bit like proving the statement "all odd numbers are prime" by saying "$5$is odd and prime". Mar2 comment In how many ways can the rooks be arranged? @Ama No - there's a white row in row 4, and it would threaten the black rook (and vice versa). Mar2 comment Intuitive description of what a topological space is?! Yes, "nearness without distance" is a good first-approximation for how to think about topological spaces. Mar2 comment In how many ways can the rooks be arranged? There are more white rooks than rows, thus at least two columns contain white rooks. So suppose at least 4 rows contain white rooks. That leaves 2 rows for the black rooks. But the black rooks cannot go in the same columns as the white rooks, thus there are at least 4 squares in those 2 rows where the black rooks cannot go. This leaves 8 squares available for the black rooks, which isn't enough. So no, one color cannot occupy more than 3 rows. Mar1 comment How is integer polynomial factorization reduced to factorization over a finite field? What about factoring over finite fields other than$\mathbb Z/p\mathbb Z$? Can that be useful? Mar1 comment How is integer polynomial factorization reduced to factorization over a finite field? Mar1 comment Are there any bases which represent all rationals in a finite number of digits? @synful I suggest trying to prove it yourself, it's very easy. Think about what multiplying by a power of$10$does to a number's decimal expansion. Feb28 comment What are these math symbols? While the current answer is a likely explanation, you won't get a real answer without more context. Are you reading this from a textbook? Could you take a picture of a page featuring these symbols (the entire page, not just the symbols). Feb28 asked How is integer polynomial factorization reduced to factorization over a finite field? Feb26 revised How to visualize the Cartesian product of a set and an interval edited tags Feb26 comment Why is Gödel's Second Incompleteness Theorem important? Sure, trusting$T$because$T'$says it's consistent is not epistemologically sound, but is trusting$T\$ just because it can prove itself consistent any better? Is that not some form of circular reasoning? Self-proving consistency has the advantage of being amenable to a precise mathematical definition, but that doesn't necessarily make it philosophically useful...