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21h

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New algorithm discovered to find prime numbers
How can I make myself clearer? NO! This is not an appropriate use of MO! 
21h

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What is the technical difference between a deformation and a perturbation?
I feel diffident saying this, since you've done plenty of work in which the word "deformation" is embedded (perhaps esp. in algebra where the name Gerstenhaber is also prominent), but these words appear in varying contexts. Is there a particular context in which you see both words being used, where a technical distinction would become important? 
22h

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New algorithm discovered to find prime numbers
It's been put on hold and it will probably remain so according to the judgment of the community. Please read the help center (linked to above) for information on what questions are considered ontopic here. 
23h

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New algorithm discovered to find prime numbers
If you have a specific mathematical question that is geared to research at the PhD level and beyond, then that is what MathOverflow is for. We don't handle questions that ask how to announce results, and we are not a bulletin board for such announcements. 
23h

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Are hyperreal numbers isomorphic to formal power series?
@JoelDavidHamkins I was confused it seems; thanks for setting me straight! I'm going to use my mod powers to edit my comment now. 
1d

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Are hyperreal numbers isomorphic to formal power series?
Anixx, I think a problem here is exactly how you are defining the order if you are considering $x$ to be infinite and considering power series expressions such as $\sin x$. Is this going to be positive or negative (or zero)? I think you have to be careful here! 
1d

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Are hyperreal numbers isomorphic to formal power series?
Oh, I see (and sorry I was confusing). Right, the way that Puiseux series are usually set up, the $x$ will be infinitesimal [I edited a mistake here in my answer; I often get confused which way it should go], and there, there is no such series for that would express an infinite element such as $e^y$ where $y = x^{1}$. 
1d

revised 
Are hyperreal numbers isomorphic to formal power series?
added 6 characters in body 
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Are hyperreal numbers isomorphic to formal power series?
Yes, $\sin \omega$ will be infinitesimal. 
1d

revised 
Are hyperreal numbers isomorphic to formal power series?
added 186 characters in body 
1d

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Are hyperreal numbers isomorphic to formal power series?
(1) No, you can form a hypperreal $\sin \omega$. (2) Yes, one can regard the field of formal power series as an ordered subfield of the hyperreals. 
1d

answered  Are hyperreal numbers isomorphic to formal power series? 
1d

awarded  Nice Answer 
1d

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Examples of categorical adjunctions in analysis, Lie theory, and differential geometry?
The second example also reminds me of an interesting result due to Schanuel, described here: ncatlab.org/nlab/show/bornological+set#properties 
2d

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morphism from a compact group to Z ?
This is really a proof from the Book. Thanks very much. 
2d

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Proofs without words
köszönöm, Google Translate. 
2d

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Proofs without words
It might be noted that the success of the illusion partly depends on the fact this uses Fibonacci numbers (it is a coincidence I guess that the next newest answer is also about Fibonacci numbers!). 
2d

answered  Examples of categorical adjunctions in analysis, Lie theory, and differential geometry? 
2d

revised 
Do homsets really live in the category Set?
added a link to the M.SE question 
2d

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Do homsets really live in the category Set?
By the way, it's "ETCS" (Elementary Theory of the Category of Sets), not "ECTS". I went ahead and edited the two places where I spotted the typo. 