Recent content by VeeEight

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    Courses How hard are upper division courses compared to calculus?

    That course sounds like the book Elements of Modern Algebra by Gilbert. Maybe check it out and compare it with a standard 4th year algebra text in Dummit/Foote where you will go into more details of groups/rings/fields and then more advanced topics in algebra.
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    Why Is the Heine-Borel Theorem Unique to ℝ?

    You should have asked him for a proof. Every compact metric space is separable.
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    Is the Countable Complement Topology a Valid Topology on the Real Line?

    This is not true. This is not true either To show it is a topology, set up your usual arbitrary union of open sets and take the complement in X. There is a set theory identity you use here to show that is it countable. Do the same for the finite intersection of open sets. This is essentially...
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    Why Is the Heine-Borel Theorem Unique to ℝ?

    It is complete. You'll want to consider sets that are not just bounded but totally bounded (or pre-compact).
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    Can commutativity of multiplication and addition under real numbers be assumed?

    You are correct in your reasoning. If x*y = x+y + xy, then y*x = x+y +yx, which holds since addition and multiplication are commutative in the reals.
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    Open set challenging question and mind-blogging conceptWelcome.

    Two possibilities have been eliminated. It's not hard to find the answer, and to deduct the reason for it (although the definitions are made precise so you can solve this kind of problem by going back to your notes)
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    Can a Countable Intersection of Infinitesimal Balls be Bounded Away from 0?

    Really? Z, Q? Each of your open balls are bounded, so wouldn't the intersection be bounded? I admit I know nothing of nsa, but I don't precisely see the question.
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    Rectangle question and closure of the interior?

    You are being asked to show that Q = Cl (IntQ) You know how to define Int and Bd, so write out the definitions explicitly (in set theory notation) to show that they coincide.
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    How to Prove Common Divisors Divide the G.C.D.?

    Do you know the formula for gcd involving lcm? Try using that.
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    Rings and Fields - Write down the nine elements of F9

    You are told that F9 = {a+bi | a,b in F9}. The first part is asking you to try out all the elements. So for example, 1+2i is an element. The second part is asking you to show that for all a+bi in F9, there is some c+di such that (a+bi)(c+di) = 1. Try writing the inverse out using a and b in some...
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    Proving bx=c Can Never Have a Single Solution in R

    b is a zero divisor seems to be important. Try using that by left multiplying bx by non zero y where yb = 0.
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    Proving the GCD Property: A Challenge for Algebra Students

    Use the Euclidean algorithm.
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    What are some insightful quotations about topology?

    Ed Whitten? Try quoting someone smart!
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    What Function Types and Inverses Can Exist Between Different Cardinalities?

    I'm assuming he means the standard Euclidean topology
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    Proving Equivalence of Standard and Basis-Generated Topologies on RxR

    What are you having trouble understanding? What is the natural metric topology of R? This is essentially the same that is put on RxR, pointwise. Can you see how this coincides with open disks? It is not a hard problem.
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