Recent content by SYoungblood

Real #s is the best notation I could think of for the set of Real Numbers. The set (2,3] is neither open nor closed under open topology, which I noted as U, in the fashion of my test. Cl is a closed space. As an example, in the space (Real #s, U), Cl((0,1)) = [0,1], the compliment of the...

Homework Statement Hello All, I am experiencing Adventures in Topology. So far, so good, but I have an issue here. In the topological space (Real #s, U), show that 1 is not an element of Cl((2,3]).Homework Equations The closed subsets of our topological space are the converses of the given...

Thank you, SY

Perhaps a supporting example -- we have (0,1) as an open set, while [0,1] is a closed set. Both (0,1] and [0,1) are neither open nor closed.

My topology book hasn't talked about discrete topology (yet, it's still early on in the course). How could it be open if the set has bounds like the compliment given above? Thank you, SY

Homework Statement [/B] Is {n} an open set?Homework Equations [/B] To use an example, for any n that is an integer, is {10} an open set, closet set, or neither?The Attempt at a Solution [/B] I say {10} is a closed set, because it has upper and lower bounds right at 10; in other words, it is...

I was able to figure it out. Th actual question is to find the final hex digit of 1! + 2! + 3! + ... + 1000! Since, as you said, we accumulate zeroes in summing factorials at every fifth element (4!=24; 5!=120, 9!=362,880 10!=3,628,800...) we only need to find the values up to 20! (For the...

GAAH. I see what you got -- we will have a large number of zeroes (I'm too lazy to figure out how many) -- certainly more than four, which establishes divisibility by 16, and then we convert to hex. Thank you, SY

Homework Statement Hello all, I am trying to determine the last hexadecimal digit of a sum of rather large factorials. To start, I have the sum 990! + 991! +...+1000!. I am trying to find the last hex digit of a larger sum than this, but I think all I need is a push in the right direction...

I got it, this and breaking out my old LA text helped. Thank you. SY

Homework Statement Let X=ℝ3 and let V={(a,b,c) such that a2+b2=c2}. Is V a subspace of X? If so, what dimensions? Homework Equations A vector space V exists over a field F if V is an abelian group under addition, and if for each a ∈ F and v ∈ V, there is an element av ∈ V such that all of...

LCKurtz, I just wanted to say thank you for your time. I spoke to a principal in the district that I work in who has an. MS in mathematics, and he was able to give me a good bit of sorely needed direction.

Still work in progress... Again, thank you. SY

OK, as I have my breakfast and coffee, I honestly think that I have gone backwards here. The fist part of my question deals solely with addition, so that is the only operation I will look at right now. We want to show the iso T:S→M, as defined by T(a+b√2)={{a 2b}{b a}}. The function b is...

So, T(x+y) maps to T(a)+T(b√2)⊕T{a 2b}{b a}}? For multiplication, T(xy) maps to T(a)T(b√2)⊗T{a 2b}{b a}}, and we still have closure by writing x in matrix form and multiplying a 1x2 matrix by a 2x2 matrix? As far as the iso not being preserved under multiplication, I am inclined to guess...