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visits member for 2 years, 4 months
seen 2 days ago

when someone smiles at me, all I see is an ape bearing its teethe


Jul
2
comment Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$
On line two of your proof I think you meant "in $Y$" not "in $X$". Also could you explain how it follows that in these two disjoint open sets in $Y$ we always have $f(y) > g(z)$ for any $y\in U_1$ and $z\in U_2$? I don't see how this follows from what you have above it. Thanks.
Jul
1
comment Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$
I certainly believe you, I just wonder if maybe there is an error in the book and parts (a) and (b) were switched. Anyways thanks for the help, I should hopefully be able to figure it out from here.
Jul
1
comment Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$
This is part (b) of the problem almost word for word, my problem is part (a), I'm not sure what to make of that.. Except that they use min instead of max.
Jul
1
asked Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$
Jul
1
comment Have there been efforts to introduce non Greek or Latin alphabets into mathematics?
+1 for suggesting katakana.
Jul
1
accepted Possible errors in my professor's notes, Abel summation
Jul
1
comment Possible errors in my professor's notes, Abel summation
Ohhhhh that's right! Ok cool thanks.
Jul
1
comment Possible errors in my professor's notes, Abel summation
I made an edit 14min ago it's the 1 to t integrals that are the problem, not the 1 to N.. not sure if you saw that or not. The reason is that B(1) = 1/2 when you want the lower bound to give zero since B(t) = {t} - 1/2 by itself
Jul
1
revised Possible errors in my professor's notes, Abel summation
edited body
Jul
1
asked Possible errors in my professor's notes, Abel summation
Jun
29
comment If $K$ is an extension field of $\mathbb{Q}$ such that $[K:\mathbb{Q}]=2$, prove that $K=\mathbb{Q}(\sqrt{d})$ for some square free integer $d$
Thanks! This makes sense.
Jun
29
accepted If $K$ is an extension field of $\mathbb{Q}$ such that $[K:\mathbb{Q}]=2$, prove that $K=\mathbb{Q}(\sqrt{d})$ for some square free integer $d$
Jun
29
comment If $K$ is an extension field of $\mathbb{Q}$ such that $[K:\mathbb{Q}]=2$, prove that $K=\mathbb{Q}(\sqrt{d})$ for some square free integer $d$
I'm vexed by Zarrax's and Dylan's comments, but going off of anthonyquas if I can show $\alpha^2$ is an element of the rationals than $\alpha$ is a solution to the equation $x^2 - \alpha^2$ which is in $\mathbb{Q}[x]$. Is this the right direction?
Jun
29
asked If $K$ is an extension field of $\mathbb{Q}$ such that $[K:\mathbb{Q}]=2$, prove that $K=\mathbb{Q}(\sqrt{d})$ for some square free integer $d$
Jun
24
comment What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$
Thanks for this.
Jun
24
accepted What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$
Jun
24
comment What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$
Excellent, this makes complete sense, thanks.
Jun
24
asked What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$
Jun
23
accepted If $\sum a_n z^n = f(z) = \sum b_n z^n$, What Can Be Said About the Coefficients $a_n$ and $b_n$
Jun
23
comment If $\sum a_n z^n = f(z) = \sum b_n z^n$, What Can Be Said About the Coefficients $a_n$ and $b_n$
Ah that clears that up for me, thanks Martin.