Activity for DNB
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #288113 |
Post edited: |
— | over 1 year ago |
| Edit | Post #288113 | Initial revision | — | over 1 year ago |
| Question | — |
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." Are there official terms for these 2 different interpretations of the same statistic? >Lord Hoffmann and Baroness Hale advanced the following arguments against awarding damages for the pure loss of a chance of being cured: > >(1) The Hotson82 problem. In cases such as Gregg v Scott, it may well... (more) |
— | over 1 year ago |
| Comment | Post #288090 |
Many thanks! I prefer your second example. English ISN'T my first language, which is why your first example bewildered me. (more) |
— | over 1 year ago |
| Edit | Post #288101 |
Post edited: |
— | over 1 year ago |
| Edit | Post #288101 |
Post edited: |
— | over 1 year ago |
| Edit | Post #288101 | Initial revision | — | over 1 year ago |
| Question | — |
How to intuit that if you destroy someone else's lottery ticket, you didn't deprive her of a chance of winning the lottery? Despite perusing the following at least 20 times, I'm still tempted (in dereliction of the authors' advice to resist this temptation) to answer $\color{red}{\text{"Yes – though it was a very small chance"}}$ to the question whether Friend deprived Ungrateful of a chance of winning the National Lott... (more) |
— | over 1 year ago |
| Comment | Post #288090 |
Thanks. $\color{limegreen}{1.}$
Can you simplify your example of *"Imagine a tabletop roleplaying game. Your character is sneaking down a dungeon corridor. Unfortunately, you neglected to check for traps, and a poison dart flies out of a concealed hole. You roll the dice to avoid it, but you only h... (more) |
— | over 1 year ago |
| Edit | Post #288087 |
Post edited: |
— | over 1 year ago |
| Edit | Post #288087 |
Post edited: |
— | over 1 year ago |
| Edit | Post #288087 | Initial revision | — | over 1 year ago |
| Question | — |
25% probability that there was a chance of avoiding injury $\quad$ vs. $\quad$ 25% chance of avoiding injury I ask about merely the math behind the last sentence of footnote 71 quoted below. I quote the legalistic sentences thereinbefore for context, but they may be immaterial. How does "a 25% probability that there was a chance of avoiding injury" differ from "25% chance of avoiding injury"? Alas, my mi... (more) |
— | over 1 year ago |
| Edit | Post #286453 | Initial revision | — | over 2 years ago |
| Answer | — |
A: $g(x)\xrightarrow{x\to\infty}\infty$ Implies $g'(x)\leq g^{1+\varepsilon}(x)$ Consider $g^{-\epsilon}$. Then its first derivative is $Dx \\; g^{-\epsilon} = \epsilon g^{-1-\epsilon} g'$. Then $g^{-\epsilon} > 0$ and tends to 0, and ${Dx \\; g^{-\epsilon}} < 0 $. If $Dx \\; g^{-\epsilon} < -\epsilon$ on a set of infinite measure, then $\int^{x}0 Dx \, g^{-\epsilon} \quad dx ... (more) |
— | over 2 years ago |
| Edit | Post #285679 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285679 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285679 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285679 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285679 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285679 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285679 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285680 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285680 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285680 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285680 |
Post edited: |
— | almost 3 years ago |
| Comment | Post #285681 |
Thanks. How can you rewrite the Generalized Vandermonde's Identity with a Summation Index, and Upper and Limits of Summation like Rothe-Hagen Identity? (more) |
— | almost 3 years ago |
| Edit | Post #285691 | Initial revision | — | almost 3 years ago |
| Question | — |
Why ways to pick a 2-person committee from 4 people $3!$? Why aren't ways to form a 3-member committee from 8 people $8 \times 7 \times 6$? Why was https://math.codidact.com/posts/285679 closed as duplicate of https://math.codidact.com/posts/280168? They may involve the same concept, but the questions AND ANSWERS differ! (more) |
— | almost 3 years ago |
| Edit | Post #285680 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285680 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285680 | Initial revision | — | almost 3 years ago |
| Question | — |
How can a 15 year old construe the LHS of Generalized Vandermonde's Identity, when it lacks summation limits and a summation index? Paradoxically, though Rothe-Hagen Identity (henceforth RHI) $\sum\limits{k=0}^n\frac{x}{x+kz}{x+kz \choose k}\frac{y}{y+(n-k)z}{y+(n-k)z \choose n-k}=\frac{x+y}{x+y+nz}{x+y+nz \choose n}$ generalizes Generalized Vandermonde's Identity (henceforth GVI), $\sum\limits{k1+\cdots +kp = m} {n1\c... (more) |
— | almost 3 years ago |
| Edit | Post #285679 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285679 | Initial revision | — | almost 3 years ago |
| Question | — |
How to intuit, construe multiplicands and multiplicators $\le 10$ resulting from $\dbinom pc$, WITHOUT division or factorials? I grok, am NOT asking about, the answers below. Rather — how can I deduce and intuit the multiplicands and multiplicators $\le 10$, resulting from simplifying $\dbinom {p \text{ people}}{c\text{-person committee}}$ DIRECTLY? WITHOUT division or factorials! Orange underline 1. Unquestionably... (more) |
— | almost 3 years ago |
| Comment | Post #285670 |
I have, but I haven't found an expatiation of multiplication vs. addition. Most books merely present the rule and expect you to memorize it. (more) |
— | almost 3 years ago |
| Edit | Post #285672 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285671 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285672 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285672 | Initial revision | — | almost 3 years ago |
| Question | — |
To correct for overcounting, why can't we divide by the sum of the over-counts? The book doesn't expatiate the sentence underlined in red below. 1. Why "it isn't 2 + 2"? 2. Note that $2 \times 2 = 2 + 2 = 4$! Is this a coincidence? >Problem 3.4: How many distinct arrangements are there of PAPA? > >Image alt text David Patrick, BS Math & Computer Science, MS Math (C... (more) |
— | almost 3 years ago |
| Edit | Post #285671 | Initial revision | — | almost 3 years ago |
| Question | — |
How can you "easily see that such squares [of side length $\sqrt{13}$ and $\sqrt{18}$] will not fit into the [4 × 4] grid"? >Problem 2.4: How many squares of any size can be formed by connecting dots in the grid shown in Figure 2.2. I skip p 31, but apprise me if you want me to include it. 1. Side lengths of squares must be equal. Thus how can $m \neq n$ below? 2. How do you most "easily see that such squares wil... (more) |
— | almost 3 years ago |
| Edit | Post #285670 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285670 | Initial revision | — | almost 3 years ago |
| Question | — |
Why 1. multiply the number of independent options? 2. add the number of exclusive options? Ironically, this textbook highlights understanding over memorization, but it doesn't expatiate the two WHY's in the question title! >When faced with a series of independent choices, one after the other, we multiply the number of options at each step. When faced with exclusive options (meaning ... (more) |
— | almost 3 years ago |
| Edit | Post #285596 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285443 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #285613 | Initial revision | — | almost 3 years ago |