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Activity for Chgg Clou‭

Type On... Excerpt Status Date
Edit Post #280847 Post edited:
15 days ago
Edit Post #280847 Post edited:
15 days ago
Comment Post #285447 thanks for your reply. I corrected my post. I don't want 0 as the answer. As an investor, I covet exposure to AT LEAST 1 water ETF. Feel free to edit my post. I afraid that if I generalize or broaden my question into a pure math problem, I won't understand it!
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18 days ago
Edit Post #285447 Post edited:
18 days ago
Edit Post #285447 Initial revision 18 days ago
Question How to deduce which ETF is redundant? a of ETF1's holdings in ETF3, a of ETF2 in ETF3, b of ETF1 are in ETF2, b of ETF2 in ETF1.
According to https://www.etfrc.com/funds/overlap.php, 1. 47.2% of FIW's 37 holdings $\in$ AQWA's 38 holdings. 2. 47.2% of PHO's 36 holdings $\in$ AQWA. 3. 77.8% FIW's holdings $\in$ PHO. 4. 77.8% PHO's holdings $\in$ FIW. My two goals. I must 5. buy $\ge 1$ Water ETF, such as the 3 a...
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18 days ago
Comment Post #285436 [Cross posted](https://redd.it/rsxhhw) on r/mathematics, that has gotten 16 comments so far.
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19 days ago
Edit Post #285342 Post edited:
30 days ago
Edit Post #285342 Post edited:
30 days ago
Edit Post #285344 Initial revision 30 days ago
Question How can you analogize mathematical induction to dominoes falling, if some domino can fail to topple?
This analogy doesn't convince me, because what if some domino (after b, the base case) fails to topple? In real life, a domino can remain standing upright if it got placed too far apart from the previous domino — or if the previous domino didn't hit this steadfast domino with sufficient force (to top...
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30 days ago
Edit Post #285342 Initial revision 30 days ago
Question Is Mathematical Induction truly "induction", or misnamed?
By induction, I mean this screenshot from this Youtube video ![](https://i.stack.imgur.com/s8VJy.png) Abduction as an Aspect of Retroduction | Chiasson, Phyllis | Commens > Induction: > The prefix “in,” also from the Latin has to do with inclusion. Thus, the prefix “in” (to include) combi...
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30 days ago
Edit Post #285326 Initial revision about 1 month ago
Question Why must percent change divide the difference by the old, NOT new, value?
![](https://www.onlinemathlearning.com/image-files/percent-change.png) My 14 year old still cannot intuit why the denominator must be the old number, not the new — not even after reading the answers on Math SE. Can someone explain this better?
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about 1 month ago
Edit Post #285005 Post edited:
about 2 months ago
Edit Post #285014 Post edited:
about 2 months ago
Comment Post #285005 I have the same question as https://math.stackexchange.com/a/2667399, but I'm seeking a better explanation than cakes and pieces of cake.
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about 2 months ago
Edit Post #285015 Post edited:
about 2 months ago
Edit Post #285015 Post edited:
about 2 months ago
Edit Post #285015 Post edited:
about 2 months ago
Edit Post #285015 Post edited:
about 2 months ago
Edit Post #285015 Initial revision about 2 months ago
Question Intuitively, why can $a, b$ cycle in ${\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}$?
I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ 1. Rather, what's the intuition why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator? 2. What's this phenomenon or behavior calle...
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about 2 months ago
Edit Post #285005 Post edited:
about 2 months ago
Edit Post #285005 Post edited:
about 2 months ago
Edit Post #285005 Post edited:
about 2 months ago
Edit Post #285005 Post edited:
about 2 months ago
Edit Post #285014 Initial revision about 2 months ago
Question How can Cross Multiplication be intuited or pictured? average(average(a,b),c) vs. average(a,average(b,c)).
Why were my two questions closed? Moderator Peter Taylor's comments feel dissimulating. >I can't even guess at what you're asking. But another user r understood my question. >If the question is "Why does dividing two equal things by the same thing give two equal things" then I'm not sure why...
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about 2 months ago
Edit Post #285005 Post edited:
about 2 months ago
Comment Post #284997 "CD is not a dumping ground for your rejected, low-effort questions." This is unmannerly. And you're assuming without evidence I'm that inquirer on Stack Exchange, that can unjustifiably close excellent questions.
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about 2 months ago
Edit Post #284997 Post edited:
about 2 months ago
Edit Post #284997 Post edited:
about 2 months ago
Edit Post #285005 Initial revision about 2 months ago
Question How can Cross Multiplication be intuited or pictured?
Image alt text I already know, I'm NOT asking about, the algebra. It's NOT intuitive why 3 pears x 4 tangelos = 6 quinces x 2 riberries $\iff$ 3 pears/6 quinces = 2 riberries/4 tangelos. I stumbled the picture below, but how does it proffer intuition? ![](https://dr282zn36sxxg.cloudfront.n...
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about 2 months ago
Edit Post #284997 Initial revision about 2 months ago
Question Without trial and error, average(average(a,b),c) vs. average(a,average(b,c)).
EXCLUDE Trial and Error. If $a = b = c = 0$, then obviously both sides are equal. My child is 14 y.o. We prefer pretty proofs by picture (but beware), AND intuition! Recondite algebra is not required. But how do I systematically deduce when $\overline{\overline{a, b}, c} = \frac{a}{4}+ \frac{b}{...
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about 2 months ago
Edit Post #283385 Post edited:
5 months ago
Edit Post #283385 Initial revision 5 months ago
Question How does counting E twice explain the discrepancy between the third between C and E, third between E and G v. fifth between C and G?
I still don't grasp the "source of the discrepancy". "the E got counted twice when we went C,D,E and then E,F,G, but only got counted once when we went C,D,E,F,G." — So what? How does this expound the discrepancy? Impaled on a Fencepost | > The music theorists of the Middle Ages committed a fe...
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5 months ago
Comment Post #283372 @#54204g Yes! Great picture! Looking forward to your answer.
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5 months ago
Edit Post #283372 Post edited:
5 months ago
Edit Post #283372 Post edited:
5 months ago
Edit Post #283372 Post edited:
5 months ago
Edit Post #283372 Initial revision 5 months ago
Question How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(b - a)}{{\color{red}{-}}(d - c)} \equiv \dfrac{b - a}{d - c}$?
I'm not asking about algebra here which I can effortlessly effectuate. If helpful, let's intuit subtraction as facing backward, and the negative sign as backward steps. How does this intuition assist us to intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(b - a)}{{\color{red}{-}}(d - c)} \e...
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5 months ago
Edit Post #282600 Initial revision 6 months ago
Question Why so many books on introduction or bridges to proofs for undergraduates?
The two quotes that I embolded below substantiate there are too many books that allegedly assist undergraduates to transition to proofs. If these authors and publishers are desperate for income, wouldn't they profit more from writing solutions (like John Weatherwax Ph.D. (MIT)) to books that don't ...
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6 months ago
Edit Post #282522 Initial revision 7 months ago
Question How can Abraham Wald's approach lead you to ignore crucial features of a problem?
1. Kindly see the red sentence below. What exactly does "that approach" mean? I don't know the term for "he peered right through to the mathematical struts and nails holding the story together"? 2. How exactly does Wald's approach $\color{red}{\text{"lead you to ignore features of the problem that...
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7 months ago
Comment Post #282055 @MonicaCellio Does my edit clarify?
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8 months ago
Edit Post #282055 Post edited:
8 months ago
Edit Post #282055 Post edited:
8 months ago
Edit Post #282061 Post edited:
8 months ago
Edit Post #282061 Initial revision 8 months ago
Question How does Pr(an event next year) $= 1/100$ imply Pr(at least one of these events occurring in the next 25 years) $> 1/5$?
Please see the embolden phrase below. It appears to equalize, or at least relate, Pr(an event next year) $= 1/100$, with Pr(at least one of these events occurring in the next 25 years) $> 1/5$? But the former is an equality, whilst the latter an inequality? >     Turning to other e...
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8 months ago
Edit Post #282060 Post edited:
8 months ago
Edit Post #282060 Initial revision 8 months ago
Question Why isn't $\Pr(diseased|+ test) = \dfrac{\text{number of true positives}}{\text{number of false positives}}$?
1. Technically, the $\color{red}{10}$ quoted below should be 9.99, because $1% \times 999 = 9.99%$. Anyways, why $\Pr(diseased|+ test) = \dfrac{1 \text{ true positive}}{9.9 \text{ false positives} + \color{limegreen}{1 \text{ true positive}}}$? Why isn't $\Pr(diseased|+ test) = \dfrac{1 \text{ t...
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8 months ago
Comment Post #282038 "Then married > smokers, but now married smokers / married people is 10%, and all smokers / all people is 20% (check this yourself)." Can you please show the steps? Married smokers/married people = 10%/50% = 20%, but you wrote "10%"? "all smokers / all people" = (10% + 30%)/all people. But what numbe...
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8 months ago
Comment Post #282038 Hi! Thanks for your replies! "I wonder if you meant to write married smokers < all smokers," No I didn't. The author's sentence is "To say that marital status and smoking status are negatively correlated, for example, is simply to say that **married people [emphasis mine]** are less likely than the *...
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8 months ago
Edit Post #282056 Initial revision 8 months ago
Question What does "individuals discount the future in a constant manner" mean?
1. Is the embold phrase referring to Present Value? 2. But how does Present Value relate to the example below with the "online bookstore"? >### AMBIGUITY AND THE FUTURE >Up to now, I’ve said little about how timing affects our reaction to uncertainty. For many decision problems we do not kn...
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8 months ago
Edit Post #282055 Initial revision 8 months ago
Question How's the outcome of airplane crashes almost always certain, but the probability is not?
Please see the bolden phrase and Table 12.1 below. For plane crashes, did the author mix up which (probability or outcome) is ambiguous, and which is precise? 1. Isn't the outcome of airplane crashes AMBIGUOUS? Because they aren't fatal? But the author wrote "almost always certain". And in Tab...
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8 months ago
Edit Post #282049 Post edited:
8 months ago
Edit Post #282052 Initial revision 8 months ago
Question If money's less valuable in the two-bullet case of the Russian Roulette problem, then ought you pay more to remove a bullet when the gun has $\ge 2$ bullets?
The emboldened sentences feel contradictory. On one hand, "they are equal reductions in the probability of death". On the other, "money is less valuable in the two-bullet case since they are 1/6 likely to die anyway". What does this imply for the two-bullet case? Ouoght you pay more to remove a bulle...
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8 months ago
Edit Post #282051 Post edited:
8 months ago
Edit Post #282051 Initial revision 8 months ago
Question Why should the near-zero prior probability, of 9/11/2001 attacks on the World Trade Centre, overwhelm any subsequent response that may have lowered the objective risk?
Can you please expound the embold phrase below? Can this be calculated? >&nbsp; &nbsp; &nbsp; It is notoriously difficult, however, to assess what one’s prior assessment of the risk would have been had one thought of the event before it actually occurred. Most Americans had never contemplated th...
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8 months ago
Edit Post #282049 Post edited:
8 months ago
Edit Post #282049 Initial revision 8 months ago
Question Why paradoxical to accept \$3, and avoid betting on Dushanbe's temperature for a prize of \$10?
If you don't know Dushanbe's past or historical temperatures, then isn't it rational to accept the $3 for sure? It doesn't feel rational to bet whether the temperature's low or high in Dushanbe, when you have no clue which side is more probable. I don't understand why there's a paradox. If you kn...
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8 months ago
Edit Post #282046 Post edited:
8 months ago
Edit Post #282047 Initial revision 8 months ago
Question Why's the unique sub-game perfect equilibrium, that the first player should offer around $1.25 to player 2?
Please see the bolden phrase below. Let's abbreviate player $j$ to $Pj$. Even if this is the unique sub-game perfect equilibrium, it feels unnecessarily risky and irrational to me. Why wouldn't you simply offer $2.5 (50% of 5) to P2? You don't know if P2 is rational, reasonable, or sane. I can't ...
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8 months ago
Edit Post #282046 Initial revision 8 months ago
Question Why rational to be indifferent between two urns, when urn A has 50-50 red and white balls, but you don't know urn B's ratio?
Please see the embolden sentence below. Assume that I'm risk adverse and "prefer the known chance over the unknown". Why's it irrational for me to choose A? >&nbsp; &nbsp; &nbsp; Also, there were problems on the probability side. One famous debate concerned a paradox posed by Daniel Ellsberg (of l...
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8 months ago
Edit Post #282031 Post edited:
8 months ago
Edit Post #282031 Post edited:
8 months ago
Edit Post #282031 Initial revision 8 months ago
Question Why are you permitted to define $1 − 1 + 1 − 1 + . . .$?
Please see the embold phrase below. Why doesn't $1 − 1 + 1 − 1 + . . .$ possess an intrinsic, Platonic objective meaning? The best way to showcase my confusion, is to burlesque the Riemann Hypothesis. If Hardy and humans can simply define $1 − 1 + 1 − 1 + . . .$, why not just define $\zeta(s)=\sum{...
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8 months ago
Edit Post #282020 Initial revision 8 months ago
Question What was Justice Scalia's mathematical mistake in Penry v. Lynaugh (1989)?
Please see the bolden phrase below. Please don't hesitate to reduce the amount of quotation, which I know is lengthy, whilst preserving enough context. >&nbsp; &nbsp; &nbsp; But even granting this point, Scalia writes, state legislatures have not demonstrated a national consensus against executi...
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8 months ago
Edit Post #282016 Initial revision 8 months ago
Question Why mustn't the proportion of smokers among married people be the same as the proportion of smokers in the whole population?
Please see the embolded phrase below. When I read this for the first time, I didn't see this problem at all, and this problem didn't present itself immediately to me. After rereading this four times, I still don't understand this immediate problem! >&nbsp; &nbsp; &nbsp; If you multiply both sides ...
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8 months ago
Edit Post #282015 Initial revision 8 months ago
Question How to intuit : married smokers × all people < all smokers × all married people ?
How can I intuit inequality (3) in my previous post? The author intuits inequalities (1) and (2), but not (3). Scilicet, how can you explain inequality (3) to a 10 year old? I can't intuit the meaning of multiplying smokers $\times$ people! >&nbsp; &nbsp; &nbsp; If you multiply both sides of ...
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8 months ago
Edit Post #282014 Initial revision 8 months ago
Question How to quantify "married people are less likely than the average person to smoke", "smokers are less likely than the average person to be married"?
When I first saw inequalities (1) and (2) below, I quantified them as: $\color{red}{\text{1.1. married people &nbsp; &nbsp; &nbsp; When you’re comparing two binary variables, correlation takes on a particularly simple form. To say that marital status and smoking status are negatively correlated,...
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8 months ago
Edit Post #282013 Post edited:
8 months ago
Edit Post #282013 Initial revision 8 months ago
Question Why do 3D mental pictures usually suffice for high-dimensional geometry?
Kindly see the embolded phrases below. The author doesn't expound why the 3D "mental pictures" are "usually enough". Scilicet, why doesn't "this impoverished vision" hinder high-dimensional geometry, or at least deprive or forestall you from learning all about it? >&nbsp; &nbsp; &nbsp; In the sam...
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8 months ago
Edit Post #282012 Initial revision 8 months ago
Question How can you foretell if a problem is one whose solution admits a simple mathematical description?
Kindly see the emboldened phrase below. What kind of problems is the author referring to? >### THE UNREASONABLE EFFECTIVENESS OF CLASSICAL GEOMETRY >&nbsp; &nbsp; &nbsp; For Apollonius and the Greek geometers, ellipses were conic sections: surfaces obtained by slicing a cone along a plane. ...
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8 months ago
Edit Post #281008 Initial revision 11 months ago
Question If a repair on a vessel costs $2$ and fully repaired vessel is worth $1$, don't we need know worth of broken vessel to decide whether to repair?
I divided all prices by 100,000 to simplify the question. The book beneath doesn't stipulate the current value of the vessel. But don't we need to know it, to calculate if it's worth repairing? How do we prove that regardless of the vessel's current cost, the vessel not worth repair? McKendrick. ...
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11 months ago
Edit Post #281007 Initial revision 11 months ago
Question What kind of logic does “Logic in the Theory and Practice of Lawmaking” employ?
I stumbled on 2016 Springer book Logic in the Theory and Practice of Lawmaking. I was curious and leafed through. > ![enter image description here](https://i.stack.imgur.com/9Uiqm.jpg) 1. What kind of logic is this? I scanned just the pages with the most logic symbols. 2. What level and s...
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11 months ago
Edit Post #281006 Initial revision 11 months ago
Question In If and Only If Proofs, why's the proof for one direction easier than the other?
This list. this question substantiates proofs where one direction can be proved effortlessly, but the other direction is grueling to prove. Why? If two propositions are equivalent, wouldn't their proofs have the same level of difficulty? Please don't troll with frivolous "proofs" like 'Fermat's l...
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11 months ago
Edit Post #281005 Initial revision 11 months ago
Question Intuitively, why's X% of Y = Y% of X?
I didn't spot this trick until I read this: >LPT: X percent of Y is equal to Y percent of X. > I know that multiplication is commutative. Indubitably, $\dfrac{X}{100}Y= X\dfrac{Y}{100}$ But this algebra doesn't betray the intuition! How can this be intuited?
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11 months ago
Edit Post #280850 Initial revision 11 months ago
Question How to visualize division as splitting Dividend into B equal “partial groups”, then rounding up A partial groups to get a full group?
Because $10 \div \dfrac{4}{3}$ isn't an integer, I changed the numbers in this Reddit post. My $X = 6, A = 2, B = 3$. Undoubtedly, I know $6 \div \dfrac{2}{3} = 6 \times \dfrac{3}{2} = 9$, but don't use $\dfrac{a}{b} \div \dfrac{c}{d} \equiv \dfrac{a}{b} \times \dfrac{d}{c}$ here to explain. > ...
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11 months ago
Edit Post #280849 Initial revision 11 months ago
Question How can I visualize dividing by a fraction as partial and full groups?
I can't visualize all these "full groups" and "partial groups." Can someone please picture them? Please see my questions red in-line. Please don't use the identity that $\dfrac{a}{b} \div \dfrac{c}{d} \equiv \dfrac{a}{b} \times \dfrac{d}{c} $. Because $10 ÷ 4/3$ isn't an integer, I changed the num...
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11 months ago
Edit Post #280848 Initial revision 11 months ago
Question How can I visualize this Compound Interest Chart with indefinite integrals?
How can I visualize the integrals below? Can someone draw on the chart and point to where $\int 1 \, dx = x$, $\int x \, dx = \frac 12 x^2 $, ... are ? I don't know which of these charts are more intuitive, and I'll copy and paste two. Is this called a Bar Chart? ![enter image description here][1]...
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11 months ago
Edit Post #280847 Post edited:
11 months ago
Edit Post #280847 Initial revision 11 months ago
Question How can I re-write or supplant “basis point” UNambiguously?
For this question, please DON'T use or even allude to "basis point" in your rewording, because I'm trying to replace "basis point"! "basis point" befuddles me! Basis Point (BPS) Definition > One basis point is equivalent to 0.01% (1/100th of a percent) or 0.0001 in decimal form. Please pe...
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11 months ago
Edit Post #279400 Post edited:
about 1 year ago
Edit Post #279400 Post edited:
about 1 year ago
Edit Post #279400 Initial revision about 1 year ago
Question Intuitively, what does the 1 mean in $\dfrac{a}{b} = \dfrac{1}{\frac{b}{a}}$?
For intuition, I instantiate variables with fruits: $a$ as apple and $b$ as berry (pick whatever berry you like). In terms of apples and/or berries, what does the red $\color{red}{1}$ below mean? What's the unit of $\color{red}{1}$? $\dfrac{a}{b} \quad = \quad\dfrac{\color{red}{1}}{\dfrac{...
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about 1 year ago