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7h
reviewed Reopen The existence of a smooth functions taking values $0$ and $1$ on two given closed sets
7h
reviewed Reopen analytical solution of non-linear least square problem
7h
reviewed Close Prove that in the procedure Graham-Scan, points p1 and pm must be vertices of CH(Q)
7h
answered Are sequences properly denoted as $\subset$ of a set, or $\in$ a set?
8h
revised Are sequences properly denoted as $\subset$ of a set, or $\in$ a set?
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8h
comment Is this proof by induction that $|\Bbb Q^n|=\aleph_0$ correct?
@YoTengoUnLCD: No, it's not true. $\prod_{n\in\Bbb N}\Bbb N=\Bbb{N^N}$ and it is uncountable.
8h
comment A set is finite, then there exists a bijective map from the set to some natural number?
I prefer Jech's terminology from "The Axiom of Choice", where Tarski-finite was a set where every non-empty chain of subsets has a min/max element. Then you can show that finite implies Tarski-finite implies Dedekind-finite, but without choice none of the implications are reversible. Assigning "Tarski-finite" to something which is provably finite is a waste of a good term.
12h
comment $f: B \to C$ injective $\implies \exists \hat f:A\subset B \to C$ injective.
Nothing that a comment won't do. If $f\subseteq B\times C$, then $f|_A=f\cap A\times C$.
12h
comment $f: B \to C$ injective $\implies \exists \hat f:A\subset B \to C$ injective.
You might want to write the explicit definition of the restricted function.
12h
revised Rearrangements that never change the value of a sum
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12h
revised Does number precede structure?
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12h
revised If a function has an inverse then it is bijective?
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12h
comment Why Does The Reflection Principle Fail For Infinitely Many Sentences?
I get why my answer was downvoted, I've been here for five years and gained enough haters, sure. But I really don't get why the question was downvoted. Anyone has the slightest idea?
12h
comment If I have $N_k\subset \Bbb N$ a finite subset of $k$ elements, what is the justification to saying I can relable it's elements so they are ordered?
I'm not sure what you mean. The natural numbers are ordered. $1<2<3<\ldots$ and so on. So any set of natural numbers inherits that linear ordering automatically. Since sets are agnostic to how you list their elements, you might as well list them according to their natural order.
13h
revised Correct Form of a Logical Statement
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13h
comment How to prove the not-so-long rays are homeomorphic to the reals?
@PyRulez: Enumerate the linear order as $a_n$, map $a_0$ to $0$, and by induction if you mapped $a_0,\ldots,a_{n-1}$, map $a_n$ to a rational which "behave the same" with the embedding so far, as $a_n$ do with $a_0,\ldots,a_{n-1}$. Density ensures we can find such rational.
14h
revised If I have $N_k\subset \Bbb N$ a finite subset of $k$ elements, what is the justification to saying I can relable it's elements so they are ordered?
edited title
14h
revised If I have $N_k\subset \Bbb N$ a finite subset of $k$ elements, what is the justification to saying I can relable it's elements so they are ordered?
edited body; edited tags
14h
answered If I have $N_k\subset \Bbb N$ a finite subset of $k$ elements, what is the justification to saying I can relable it's elements so they are ordered?
14h
comment If I have $N_k\subset \Bbb N$ a finite subset of $k$ elements, what is the justification to saying I can relable it's elements so they are ordered?
$k$ elements perhaps?