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visits member for 2 years, 10 months
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Dec
13
revised Compactness of the Hilbert cube without the Axiom of Choice
clarify the choice function F
Dec
13
accepted Compactness of the Hilbert cube without the Axiom of Choice
Dec
13
answered Compactness of the Hilbert cube without the Axiom of Choice
Dec
13
awarded  Popular Question
Dec
5
revised Formal languages with non-unique interpretations of terms
add a paragraph with some clarifications of my motivations
Dec
5
comment Formal languages with non-unique interpretations of terms
Thanks for the link. I haven't thought of multivalued functions, but one of the things that motivated my question was my impression (i am not sure and have no reference) that in the first half of the nineteenth century, in model theory or mathematical logics texts, the equality was not always interpreted as the identity, but only as an equivalence relation. Sometimes (as mentioned by François Dorais) the equivalence relation could be the one of a rewriting system.
Dec
4
comment Formal languages with non-unique interpretations of terms
@EmilJeřábek, i understand well that the equality relation is not symmetric with the $\omicron/O$ notation, this is one of the first things i tell my students. However, my impression was that it is a secondary concern, and can be addressed after the ambiguity of the notation is addressed. I felt that multi-valued interpretations are better than interpretations by sets because they would generalize the usual interpretation instead of replacing it with a new one (no need to interpret $\ln(2x)=\ln2 +\ln x =O(\ln x),\ x\to\infty$ as two relations between sets of functions).
Dec
4
asked Formal languages with non-unique interpretations of terms
Jul
2
awarded  Curious
Jun
14
comment Atiyah-MacDonald, exercise 2.11
Is Cayley-Hamilton Theorem necessary here? Is there no easier way to show that the powers of $\phi$ are linearly dependent over $A$?
May
26
revised Topological characterization of the closed interval $[0,1]$
grammar
May
26
accepted Topological characterization of the closed interval $[0,1]$
May
25
comment Topological characterization of the closed interval $[0,1]$
In other words, in some sense, $[0,1]$ is the "simplest" non-trivial absolute retract.
May
25
answered Topological characterization of the closed interval $[0,1]$
May
23
awarded  Organizer
May
23
revised Defining Multiplication in Polynomials over Rings of Matrices
add [reference-request] tag
May
23
suggested approved edit on Defining Multiplication in Polynomials over Rings of Matrices
May
10
revised Vector bundles vs principal $G$-bundles
remove "G-bundle", leave "principal G-bundle", as this is what is described
Apr
20
comment Are the higher homotopy groups of the Hawaiian earring trivial?
It is actually available publicly from the publisher's website.
Jan
30
awarded  Yearling