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May 7 |
comment |
Ultra Filter and Axiom of Choice You've strongly implied that the statement "there are no free ultrafilters" is consistent with ZF, but you haven't actually said so. Is the non-existence of free ultrafilters indeed consistent with ZF? |
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Apr 30 |
revised |
When two voters meet, they switch allegiance; might they all ally with the same candidate? added 133 characters in body |
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Apr 30 |
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When two voters meet, they switch allegiance; might they all ally with the same candidate? Apparently I was assuming (for no apparent reason) that the total number of voters is a multiple of 3. |
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Apr 30 |
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In NFU, is there a bijection between the set of all sets and the set of all one-element sets? If the function $g$ exists, then we can define the set from Russell's paradox, $R$, as $\{x | g(x) \not\subseteq x\}$. Then $R \in R$ if and only if $g(R) \not\subseteq R$ if and only if $R \not\in R$, which is a contradiction. |
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Mar 31 |
answered | When two voters meet, they switch allegiance; might they all ally with the same candidate? |
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Mar 12 |
comment |
Simplifying $3^2 + (-8\div2)$ A Google search suggests that the word "into" in this case is ambiguous and thus should be avoided. |
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Mar 12 |
answered | Simplifying $3^2 + (-8\div2)$ |
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Mar 12 |
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Simplifying $3^2 + (-8\div2)$ I believe that "by" and "into" are synonyms in this case. |
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Mar 12 |
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Limit point definition Well, there is an analogy to the limit of a sequence. $p$ is a limit point of $S$ if and only if there is a sequence in $S \setminus p$ whose limit is $p$. |
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Mar 12 |
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Dice game modelling: Lose everything on “3”, double everything on “1” or “6” If money doesn't have diminishing marginal utility for you, then it is never better to quit than to continue. The question of when to quit depends on what your utility function is. |
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Mar 11 |
answered | Is there a rational number (with denominator not greater than 200) between 15/106 and 16/113? |
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Mar 11 |
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Prime number divisibility Essentially, yes: the inverse from $\mathbb{Z}_p$ also works in this context. I just edited my answer to make the distinction between $\mathbb{Z}$ and $\mathbb{Z}_p$ clearer. I feel like the phrase "corresponding element" isn't the best term for me to use here, but hopefully it's clear what I mean. |
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Mar 11 |
revised |
Prime number divisibility Make the distinction between $\mathbb{Z}$ and $\mathbb{Z}_p$ clearer |
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Mar 11 |
answered | Prime number divisibility |
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Mar 11 |
comment |
summation of 0.5n to n It looks like $n$ must be even, and if $n = 10$, then the series is $9 + 8 + 7 + 6 + 5$. |
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Feb 18 |
revised |
Why isn't this a valid argument to the “proof” of the Axiom of Countable Choice? Tried to make it clearer that an "element of $A_n$" is an element of that set, not of the sequence |
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Feb 18 |
suggested | suggested edit on Why isn't this a valid argument to the “proof” of the Axiom of Countable Choice? |
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Feb 18 |
comment |
How can we tell if a set of axioms uniquely determines an algebraic structure? The Peano axioms in first-order logic do not uniquely define $\mathbb{N}$; the induction rule is not strong enough to rule out certain (quite strange) models of the Peano axioms. However, if you interpret the Peano axioms in second-order logic with the full semantics, then they uniquely define $\mathbb{N}$. In addition, if I remember correctly, there do exist uncomputable sets of first-order axioms that uniquely determine $\mathbb{N}$; for example, you could say that the axioms of your system are exactly the statements about $\mathbb{N}$ that are true. |
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Feb 18 |
answered | How do I understand $e^i$ which is so common? |
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Jan 8 |
comment |
Every infinite regular language has a non-regular subset? I just noticed that André Nicolas posted essentially this answer as a comment. |
