Activity for r~~
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #296091 |
Post edited: |
— | 4 months ago |
| Edit | Post #296091 | Initial revision | — | 4 months ago |
| Answer | — |
A: Are there combinatorial games $G$ such that $G+G$ is fuzzy? Yes (such games exist). A simple example is \(G = \{1\mathop| \mathop- 1\}\). If Left goes first in \(G + G\), their only move is to \(G + 1\), after which Right's only move is to \( \mathop- 1 + 1 = \), after which Left moves to 0 and wins. If Right goes first in \(G + G\), their only move... (more) |
— | 4 months ago |
| Comment | Post #295526 |
I don't suspect any of this is likely to be directly useful in a nonstandard-analysis-like framework, since one property you want in nonstandard analysis is to be able to distinguish between \\(\epsilon\\) and \\(\epsilon^2\\) terms, and \\(/\aleph_0^2 = /\aleph_0\\). (This is unavoidable in any ... (more) |
— | 7 months ago |
| Edit | Post #295526 |
Post edited: You always catch the silly mistakes after you post... |
— | 7 months ago |
| Edit | Post #295526 | Initial revision | — | 7 months ago |
| Answer | — |
A: Is there a stable/consistent extension of wheel theory to alephs? Any commutative semiring with a chosen multiplicative submonoid can be extended to a wheel of fractions. Cardinal addition and multiplication form a commutative semiring (glossing over the set/proper class distinction), so we can easily talk about the wheel of cardinal fractions with respect to t... (more) |
— | 7 months ago |
| Edit | Post #294781 | Initial revision | — | 11 months ago |
| Answer | — |
A: Is this a proper measure for irrationality? > 1. Is \(i(x)\) a valid irrationality measure (i.e. does it give a strictly positive result for all irrational numbers)? No, by Hurwitz's theorem), which states that for every irrational number \(x\), there are infinitely many relatively prime \(m\) and \(n\) such that \[ \left|x - \fra... (more) |
— | 11 months ago |
| Edit | Post #292189 |
Post edited: Be more precise about the n = 0 case |
— | about 2 years ago |
| Edit | Post #292189 |
Post edited: Yikes, missed an important minus sign! |
— | about 2 years ago |
| Comment | Post #292189 |
Done, thanks for the tip! (more) |
— | about 2 years ago |
| Edit | Post #292189 |
Post edited: Update log notation |
— | about 2 years ago |
| Edit | Post #292189 |
Post edited: |
— | about 2 years ago |
| Edit | Post #292189 |
Post edited: Simplify sigma formulas |
— | about 2 years ago |
| Edit | Post #292189 | Initial revision | — | about 2 years ago |
| Answer | — |
A: Is there a closed formula for multiplication of imaginary units in the direct limit of the Cayley-Dickson construction? You might find this paper helpful: An Alternate Cayley-Dickson Product. The author observes that while the standard product formula for the Cayley-Dickson construction leads to precisely this difficulty with finding a closed form, there are alternatives for the product that produce isomorphi... (more) |
— | about 2 years ago |
| Edit | Post #290772 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Minimal non-standard number in non-standard models of PA Quite the opposite; in no non-standard model of Peano arithmetic is there a minimal non-standard number. Consider the formula \\(\phi(x) = \left(x = 0\right) \vee \exists y \left(x = S(y)\right)\\). The first-order induction axiom for \(\phi\) is \\[ \phi(0) \wedge \forall x \bigl(\phi(x) ... (more) |
— | over 2 years ago |
| Edit | Post #290744 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Cyclical or “loop” fractals? Does the Cantor set qualify? This animation loops infinitely, and shows that you get back to where you started every time you zoom in by a factor of 3. Show animated GIF An animation of the Cantor set (more) |
— | over 2 years ago |
| Comment | Post #290318 |
Your claim is correct as written, I think.
It is the case that for most numbers, it is unknown if the number is normal. (That is, for a real number between 0 and 1 chosen uniformly, the probability that we know whether it is normal or not is 0.)
It is also the case that we know that most nu... (more) |
— | almost 3 years ago |
| Comment | Post #290305 |
But from the Atlas link it seems that unshackling yourself from a specific geometry unlocks *thousands* of new regular 4-polytopes. I don't see how this answers the question. You assert in your answer that most of those linked polytopes aren't regular but can you support that claim at all? The At... (more) |
— | almost 3 years ago |
| Comment | Post #290196 |
You probably mean to specify that M is a *connected* n-dimensional compact manifold; the nth Betti number is in fact the number of connected components if M is orientable. (more) |
— | almost 3 years ago |
| Comment | Post #290305 |
> They are the only ones aside from the 6 convex Euclidean 4-polytopes.
This can't be true; there are also 5 regular projective 4-polytopes, for example (hemi-tesseract through hemi-600-cell). I don't have deep expertise here but I don't know of any reason why the linked list from the Atlas of... (more) |
— | almost 3 years ago |
| Comment | Post #289826 |
> because what the code does is pick a random number with random.randint() for each candidate, and not have a fixed total population size.
So instead of simulating each voter making a random choice, you're choosing the number of voters for each candidate from a uniform distribution? This has a... (more) |
— | almost 3 years ago |
| Comment | Post #289826 |
Does your code vary the population size at all? You should definitely see a change in your observed probability for the same $n$ if so, which means that a formula expressed only in terms of $n$ can't be right. (more) |
— | almost 3 years ago |
| Edit | Post #289826 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #289826 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: Strange behavior in elections and pie charts > with randomized positions in the chart Implicit in this description of your model is the notion that every location for a separator line is equally likely. This doesn't describe the actual distribution of vote totals; with random voters, lines are much less likely to appear near other lines ... (more) |
— | almost 3 years ago |
| Comment | Post #289671 |
Wow, you seem pretty twisted up over the purpose of this site. This isn't a social media site. We are collaboratively building a public repository of knowledge here. Your submissions aren't primarily acts of personal expression; they are primarily bricks in an edifice of which we are all custodia... (more) |
— | about 3 years ago |
| Edit | Post #289644 |
Post edited: Embarassing; it's the chi-square distribution for stddev, not t |
— | about 3 years ago |
| Edit | Post #289644 |
Post edited: |
— | about 3 years ago |
| Edit | Post #289644 | Initial revision | — | about 3 years ago |
| Answer | — |
A: What is the formula for sample standard deviation of a small sample size? The sample standard deviation (with Bessel's correction) is defined to be the first formula in your post. It doesn't ‘become’ anything else. You were possibly remembering using the sample standard deviation in an estimator for the population mean. The \(t\)-value is multiplied by the sample st... (more) |
— | about 3 years ago |
| Comment | Post #288820 |
> One obvious criterion is that all the open squares be connected. If a set of squares are "walled off" with mines, then there is no way to get clues to the mines inside from the outside.
The total number of mines is known, so if there are multiple disconnected open regions but all but one of ... (more) |
— | about 3 years ago |
| Comment | Post #288168 |
Do you intend the mod to be outside the sum or inside it—i.e., are you expecting the final result to necessarily be less than M? (more) |
— | over 3 years ago |
| Edit | Post #288123 | Initial revision | — | over 3 years ago |
| Answer | — |
A: 2 construals "of 100 patients presenting with a lump like the claimant’s in Gregg v Scott, 42 will be ‘cured’ if they are treated immediately." The author of this passage is proposing a very simple hidden variable model. This model has two variables: $A$ — whether the patient has certain unknown genes (this variable is hidden) $B$ — whether the treatment succeeds (this variable is observed) And the model proposes that $A$ influenc... (more) |
— | over 3 years ago |
| Comment | Post #288087 |
I don't think being akin to a statement in predicate logic is sufficient to make a question on topic for math. Contemplating the mortality of Socrates would also be off topic, unless it was specifically asking about applying modus ponens or something. Likewise, I think it would be okay if OP were... (more) |
— | over 3 years ago |
| Comment | Post #288087 |
Not a math question. OP should perhaps ask this in a community for English language learners. (more) |
— | over 3 years ago |
| Edit | Post #288039 |
Post edited: Not a bug, but a support question. |
— | over 3 years ago |
| Suggested Edit | Post #288039 |
Suggested edit: Not a bug, but a support question. (more) |
helpful | over 3 years ago |
| Edit | Post #287975 | Initial revision | — | over 3 years ago |
| Answer | — |
A: The meaning of $\pm$ I think I would describe that as ‘the two claims $|x| = \pm x$’, not a single claim. It's comparable to saying ‘the two roots of $x^2 - 4$ are $x = \pm2$’ and not ‘the root of $x^2 - 4$ is $x = \pm2$’. Whether those two claims are meant to be and-ed or or-ed would depend on context. In a vacuu... (more) |
— | over 3 years ago |
| Edit | Post #287870 | Initial revision | — | over 3 years ago |
| Question | — |
Generalization of categorical product I'm only a dabbler in category theory; this might be a basic concept just outside of my sphere of exposure. I'm looking for references to the following universal construction, a generalization of the categorical product. Given a category $\mathcal{C}$ and a functor $F$ from $\mathcal{C}$ to... (more) |
— | over 3 years ago |
| Comment | Post #287674 |
Arguably, this numeral system is better thought of as a mixed radix system alternating between bases 5 and 4 than as a simple base-20 system. There's a valid mathematical (or maybe mathematics-educational?) question about the pros and cons of mixed radix systems versus common radix systems (I thi... (more) |
— | over 3 years ago |
| Edit | Post #287494 | Initial revision | — | almost 4 years ago |
| Answer | — |
A: Example of $f:[0,1]\to\mathbf{R}$ with $\lim_{a\to 0^+}\int_a^1f(x)dx=L $ for some real number $L$ but $\int_0^1|f(x)|dx=\infty $ Since you haven't specified that such a function needs to be continuous or well-behaved in any way, it's quite easy to describe one. The integral $\int0^1 \frac1x\,dx$ diverges, so there is an infinite amount of area to work with. Measure off the section of curve with area 1 starting at $x = 1... (more) |
— | almost 4 years ago |