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 Jul 15 asked Is it acceptable to use the term “Algebra of the Real Numbers” Jul 8 revised What's wrong with me? edited tags Jul 6 comment You see a route 14 bus on the moon. What is the most likely number of bus routes on the moon? As a school prank you release 3 greased pigs into the school with the numbers 1,2, and 4 painted in bold letters on their backs. What is the most likely number of pigs from the point of view of the school administrator? Jul 6 comment Prove in full detail that the set is a vector space @Jyrki I agree and I believe that most reasonable instructors would agree as well. However if this ambiguous wording had come up on an exam I would certainly ask the professor if we are allowed to use any theorem presented in the course. After all, there are much quicker and easier ways to prove that it is a vector space than even the subspace theorem (See Bill Dubuque's answer) Jul 6 comment Prove in full detail that the set is a vector space @Virtuoso the key phrase Prove in Full Detail suggests to me that the test wants you to show all the vector space axioms, you might be marked down on an exam if you prove by showing its a subspace. Jul 6 comment Prove in full detail that the set is a vector space @Virtuoso Typically you are not allowed to use theorems and concepts that have not been covered up to that point in class. If you are unfamiliar (i.e. it hasn't been covered yet) with the concept of a subspace then you should show all the axioms. Since a subspace is a vector space in its own right, you only need to prove that this set constitutes a subspace of $\mathbb{R}^2$ - it contains 0, closed under addition, and closed under scalar multiplication. Jul 5 asked Help Identify this Pattern in the coefficients of a polynomial Jul 1 comment Definition of Ring Vs Rng @Pete the Deskins book (well the dover reprint, I obsessively buy dover reprints for dirt cheap at used book stores) is the one I remember seeing, I was trying to track it down again but @Brian got it before me. Jun 30 accepted The mathematics behind Clebsch-Gordan Coefficients Jun 30 comment Definition of Ring Vs Rng Didn't really expect to start such debate. I haven't studied enough algebra to see the benefit of using one definition over the other. I didn't realize it was such a contentious issue. Jun 30 comment Definition of Ring Vs Rng @Pete I've also encountered some textbooks that state $1\neq0$ as a ring axiom specifically to exclude the trivial ring. Why they do that is beyond me. Jun 30 revised Definition of Ring Vs Rng added 195 characters in body Jun 30 asked Definition of Ring Vs Rng Jun 28 comment Examples of results failing in higher dimensions Proof by pictures still exists in higher math, for example see: en.wikipedia.org/wiki/Commutative_diagram . Although I agree that at the very least there is a rigor behind them. Jun 28 comment Finding $\csc$ with $\cot$ @Adam trig functions represent relations between the sides of a right triangle. Excepting some corner cases (like $\theta = \frac{\pi}{2}$) you can always construct a right triangle that "represents" the trig relation. Jun 28 comment Finding $\csc$ with $\cot$ @Adam as I pointed out in my comment, even though you checked 12 times you missed the clear arithmetic error Jun 28 comment Finding $\csc$ with $\cot$ You did everthing right, but 9+16 = 25 not 27 Jun 27 revised Number of occurrences of the digit 1 in the numbers from 0 to n added 41 characters in body Jun 27 answered Number of occurrences of the digit 1 in the numbers from 0 to n Jun 27 comment The mathematics behind Clebsch-Gordan Coefficients @Theo thanks for that, its what I get for working in a lab with a bunch of Russians - "gord-on"