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seen Jul 17 at 6:31

Discipulus sum in Iaponia.


Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
May
29
comment Constructive fixed-point theorems where finite iteration yields the fixed point
Thank you. Informally and generally speaking, Tarski's theorem yields a fixed point after an "infinite" number of applications of the function. That's unsatisfactory for my purpose.
May
23
accepted Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
May
21
comment Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
@tomasz I've assumed that the first sentence states that there exist $r$ and $s$ such that for any nonzero $f(X, Y) \in \Bbb Q(A)[X,Y]$, f(r, s) = 0. Is this how you interpreted it?
May
21
comment Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
so is it not true that for a general field extension $E/F$ and a field isomorphism $\sigma:F\rightarrow F$ there exists an extension of $\sigma$, namely, $\tau: E\rightarrow E$?
May
21
comment Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
Thank you for explaining the details. Is the algebraic closure of $\Bbb Q(A, a, b)$ necessarily $\Bbb C$? Or, can every field isomorphism be extended to one between extension field? I have the feel that such a proposition can be proved by using Zorn's Lemma.
May
21
comment Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
@tomasz I didn't think it trivial for such $r$ and $s$ to exist, so I thought the literally first sentence included something to be proved.
May
21
comment Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
@tomasz tomasz, I've assumed by the second sentence you meant the sentence that begins with "There." Now I know I was wrong. :-)
May
20
comment Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
@tomasz Could you please elaborate on that?
May
17
comment Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
@AndresCaicedo Thank you. Which of the two parts does your solution correspond to?
May
17
revised Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
added 11 characters in body
May
17
asked Existence of an automorphism of $\Bbb C$ that fixes a finite set pointwise but does not fix $\Bbb R$ setwise
May
12
accepted Why is the language of arithmetic usually $(+, \cdot, 0, s)$, not $(+, \cdot, 0, 1)$?
May
11
comment Why is the language of arithmetic usually $(+, \cdot, 0, s)$, not $(+, \cdot, 0, 1)$?
@CarlMummert what does it mean for a theory to be ambient?
May
10
comment Why is the language of arithmetic usually $(+, \cdot, 0, s)$, not $(+, \cdot, 0, 1)$?
@AndréNicolas I would be very grateful if you could elaborate on the work by Dedekind.
May
10
comment Why is the language of arithmetic usually $(+, \cdot, 0, s)$, not $(+, \cdot, 0, 1)$?
@AndréNicolas Why did Peano formalized arithmetic this way? Was the ring theory of the days of Peano different from what it is today?
May
10
asked Why is the language of arithmetic usually $(+, \cdot, 0, s)$, not $(+, \cdot, 0, 1)$?
May
7
comment Exercise in Section 2.4 of Singer & Thorpe
@TedShifrin can one say some subsequence is convergent even if the space is not metric?
May
7
asked Exercise in Section 2.4 of Singer & Thorpe