I couldn't agree more with @Steve's comment. The following response is written with elementary-to-high-school mathematics in mind. A lack of a decent number sense really does encumber making sense of ...

The (correct) sample space depends on how the probability problem has been framed: The set of letters in “$MISSISSIPPI$” is indeed $S_1=\{M,I,S,P\}.$ In a probability experiment with sample space $... View answer 6 votes Comparing the RHS of (1) and (2) one deduces that$(a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2$. First question: Is this considered an acceptable proof at a post-secondary level? It's perfectly valid to ... View answer 4 votes There is a constant difference between A's and B's ages. Here, the value of interest is constant as the input, time, varies. There is a common difference between successive terms of sequence S. Here, ... View answer 4 votes Given the equation $$\lvert2x\rvert=x-1,$$ rewriting the left-hand side as$\pm2x$results in the unique solution set$\{-1,\frac13\},$which nonetheless fails to satisfy the equation. In other words, ... View answer 4 votes The student was conflating the sum $$\frac45+\frac23$$ and the weighted average (where the weights account for group-size differences) $$\left(\frac{\color{#00F}5}{\color{#180}{5+3}}\right)\frac45+\... View answer 2 votes In statistics, business and science, I keep hearing about how precision = consistency = low variability = closeness of the data points = reproducibility & repeatability. In numerical analysis, ... View answer 2 votes Expanding my comment into an answer: So you want the umbrella term for a predicate (propositional function), like the triangle or Cauchy–Schwarz inequality, that's always true, but not necessarily so ... View answer 2 votes How about encapsulating the entirety of the explanation in a tree diagram, which is visual, accessible, and relevant to any Intro Probability classroom? We drew this today while going over the Monty ... View answer 2 votes "The function h raises 2 to the x, where x is the input" and "The function h raises 2 to the xth power, where x is the input" both ape the structure of f and g ... View answer 1 votes These two averages are of different types. Given the position function s(t) = t^2+50, what is the average velocity after 10 seconds? \frac{(10^2+50)-(0^2+50)}{10} = 10. The average velocity ... View answer 1 votes I fully agree with the self-accepted Answer, and am adding an orthogonal point: in mathematics,$$p \Leftrightarrow q \Leftrightarrow r$$is commonly understood as$$(p \Leftrightarrow q) \;\text{ and ... View answer 1 votes ✔ explaining by contrapositive Adding up any number of zeros gives zero; so, it is impossible to obtain a nonzero value by adding up just zeros. explaining by deriving contradiction Let$c$be a ... View answer 1 votes I’ve been able to inculcate students with the awareness that definitions are not just legal agreements—which they basically are—or boring fine print, by persistently demonstrating҂ using definitions ... View answer 1 votes In parts of the UK and Commonwealth countries, mixed numbers (aka mixed fractions) are commonly used till about 16 years old. So, mark schemes typically specify$5\frac14$instead of$\frac{21}4.$For ... View answer 1 votes In Mandarin Chinese, numeral: 数字 number: 号码 View answer 1 votes You might point out that the$3$-trial experiment has$8$possible outcomes and$256$possible events, which are subsets of the sample space; whereas each trial has$2$possible outcomes, which can be ... View answer 1 votes Not a proper acceptable answer, just an expansion of my original comment: A literal/direct/mechanistic recitation probably involves a lighter cognitive load than a quirkier sentence-translated ... View answer 1 votes The observation that a rhombus's diagonals bisect its internal angles gives rise to an efficient method to find an angle bisector. Here, a British national-exam question hints this method to the ... View answer 0 votes As pointed out by @AmyB and @DanielRCollins, an equation is simply a statement that two expressions are equal. @Adam remarks that the equation-identity distinction doesn't seem useful; on the contrary,... View answer 0 votes It is as cromulent (thanks, MatthewDaly!) to write $$11.40\text{ a.m.} \color{#00F}- 15\text{ min} = 11.25\text{ a.m.}$$ as it is to write$\$(4,3) \color{#00F}-\begin{pmatrix}1 \cr1\end{pmatrix}=...