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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"