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comment The empty set as an Indexing set.
Write down the definition of union and intersection. Simplify.
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comment Set of integer p-adics-Proposition
Is there any particular part of it that you don't understand? What parts of it do you understand?
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revised Quick question: G-set functor
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revised Quick question: G-set functor
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answered Quick question: G-set functor
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answered Field of algebraic reals over the rationals
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comment Ordered Field: $|x|\le y$ iff $-y\le x\le y$
@Julian: Yes: commonly, we break arguments involving absolute values by into the two parts whether $|x|$ was equal to $x$ or whether $|x|$ was equal to $-x$, so that we no longer have to deal with the absolute value signs. I believed you were trying to invoke this, but I could, of course, be entirely wrong on your intent.
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revised Ordered Field: $|x|\le y$ iff $-y\le x\le y$
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answered Ordered Field: $|x|\le y$ iff $-y\le x\le y$
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comment Quadratic Expressions: Advanced techniques of Integration
The question appears to be about the red, bolded sign $$\sqrt{9 {\mathbf{\color{red} +} } (3x-2)^2}\over 9$$
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comment Quadratic Expressions: Advanced techniques of Integration
Show the link to your wolfram alpha result: I suspect typo.
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comment Quadratic Expressions: Advanced techniques of Integration
I think you explained the wrong sign.
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answered Does there exist a unital ring whose underlying abelian group is $\mathbb{Q}^*$?
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comment Evaluate a rational function at infinity
The simplest thing to do rigorously is probably to switch to projective coordinates, then back to a different set of affine coordinates where $\infty$ is affine (i.e. set $Y=1$ rather than $Z=1$). IIRC, for actual calculation, the result is wholly analogous to simply taking the limit at infinity, subject to the simplification what $y^2 \sim x^3$ as you near $\infty$ (I'm assuming Weierstrass form), but I don't remember the fine detail at the moment well enough to explain.
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comment Evaluate a rational function at infinity
Ack, from the title I assumed you were evaluating a univariate rational function at infinity. Now that I've read your post more carefully, you have a function on an elliptic curve (represented as a bivariate function on the affine plane?), and you're evaluating that at the point at infinity of the elliptic curve!
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awarded Nice Answer
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comment What is an affine space?
@Stan: I've made an edit. (do you get pinged when I edit my post?)
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revised What is an affine space?
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answered Is there such thing as an unnormed vector space?
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answered What is an affine space?
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