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13 votes

What governs our "perception?" about the platonic realm of sets?

The recent developments on the consistency of NF bring welcome closure to the longstanding open question about whether NF was consistent. And this is naturally a very important matter for those who ...
Joel David Hamkins's user avatar
6 votes

Examples of eventual counterexamples

One could reasonably conjecture that there are no positive integers $a,b,c$ satisfying $$\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 4.$$ I say "reasonably", because the smallest ...
2 votes

Examples of eventual counterexamples

$n$ is sufficiently large for $P(a)=T$ $\forall a\in\mathbb N$ to be a 'reasonable' conjecture to make. $\ldots$ where 'reasonable' is open to interpretation I won't be too surprised if a ...
0 votes

Examples of eventual counterexamples

The word "eventually" connotes a very long sequence of positive examples before the first counterexample. Gerry Myerson points out that no polynomial of the form $x^n-1,$ when factored over $...
5 votes

Examples of eventual counterexamples

Assertion: Every integer greater than 1 can be written as the sum of a prime number and a perfect power of a nonnegative integer. The smallest (and maybe only?) counterexample to this assertion is $11^...
0 votes

what can be said about the choice of a prior in Bayesian statistics?

I haven't seen a result in the line of "the choice of a certain prior will lead to faster convergence rate" or something similar to that. If you're looking specifically for classes of ...
Durden's user avatar
  • 101
1 vote

Why is Set, and not Rel, so ubiquitous in mathematics?

One way to approach the concepts of "elements" (or "its") and "distinctions" (or "dits") is to start with the category-theoretic duality between subsets and ...

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