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Feb
5
revised Line bundles of the circle
"that that"
Feb
5
suggested approved edit on Line bundles of the circle
Jan
30
accepted Random Wolfram|Alpha identity related to $\sum_{k = 1}^{\infty}{\tan^{-1}}{\frac{1}{k^2}}$
Jan
30
comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
@user26857 Good to know, thanks.
Jan
30
revised Random Wolfram|Alpha identity related to $\sum_{k = 1}^{\infty}{\tan^{-1}}{\frac{1}{k^2}}$
edited title
Jan
29
awarded  Notable Question
Jan
27
comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
@user268578, is this why the localization you give is the "correct one"? Your method uses a set which has $(1,0)$ and $(2^k,1)$ as extra elements (which are not in the "real" multiplicative set). But the latter are all already invertible, so adding a new inverse makes no difference, and an inverse of $(1,0)$ is already going to be present, since if $r$ is the inverse of $(2,0)$, then $2r \times (1,0) = r \times (2,0) = 1$.
Jan
16
comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
For anyone stumbling upon these comments: $(0,0)$ is not the multiplicative identity! :P
Jan
16
comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
@VJP Why don't you add an answer? The hint was very helpful.
Jan
16
comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
Um, I think then every element is zero. Is this justified? $$a = a\times 1 = a\times(r\times (2,0)) = a\times(r\times (0,0)/r) = 0$$Wikipedia seems to do something similar.
Jan
16
comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
Quotients of the form $$\frac{(a,b)}{(2, 0)^n}?$$ That probably does not exclude $(1,0)$, since that can be remedied by adding a factor of $2$ to the numerator.
Jan
16
comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
i.e. as a quotient of some "well-known" ring, etc.
Jan
16
comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
@VJP Yes, I have. I haven't used it much besides proving that localizations at prime ideals are local rings. It seems that this ring is the localization of $\Bbb{R\times R}$ at the multiplicative set $$\{(1,1), (1,0), (2,0), (4,0), \ldots\}$$, but how do I describe that further?
Jan
16
comment Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
Elementwise addition and multiplication.
Jan
16
asked Adding an inverse of $(2, 0)$ to $\Bbb{R\times R}$
Jan
3
revised Good introductory book on Calculus on Manifolds
punctuation, misspelled names, "Theorum"
Jan
3
suggested approved edit on Good introductory book on Calculus on Manifolds
Dec
20
answered A question about classifying conics, from Garrity's book
Dec
20
asked A question about classifying conics, from Garrity's book
Nov
16
suggested rejected edit on Understanding differential form