Activity for tommi‭

Type	On...	Excerpt	Status	Date
Question	—	The effect of measurement accuracy and rounding on hypothesis testing I am checking the temperature I have at home with accuracy of one tenth of a grade (Celsius). The easily publicly available information is temperature in grades, with no decimals. I am doing very basic hypothesis testing: My null hypothesis is that temperatures I measure do not have a systematic b... (more)	—	5 days ago
Question	—	The derivatives of a function at a boundary point I have a function $f \colon [0, L[ \, \to \mathbb{R}$ and I want to use the derivatives of arbitrary high orders of this function at zero. The function is defined on the half-open interval $[0, L[ \, \ni 0$, for an $L >0$. Typically the derivative is only defined on interior points of an interval ... (more)	—	3 months ago
Answer	—	A: $\left(\forall \varepsilon >0: |a-b| < \varepsilon\right) \iff a=b$ vs. $\left(\forall \varepsilon > 0: a \le b + \varepsilon \right) \iff a \le b$ The absolute value version is equivalent to having both $a b - \varepsilon$, both for all positive epsilons. To see this, use the definition of the absolute value. Also, $a 0$ and $a \le b + \varepsilon$ for all $\varepsilon > 0$ are equivalent. Clearly the strict version implies the non-strict ... (more)	—	6 months ago
Answer	—	A: Is mathematical pedagogy in scope? A lot of didactics is quite mathematical, but a lot is also far from it. Stuff like different ways of understanding division or Janvier-table of transformations between different representations of functions would, to me, feel at home, while something like TPACK-model of teacher knowledge or gende... (more)	—	7 months ago
Answer	—	A: How can I choose a point from a uniform distribution within a regular polygon? A (regular, convex and some weaker condition would be sufficient) polygon is a finite union of triangles with one vertex at the origin, and which only meet at their edges. (I am being ambiguous whether I consider the triangles as closed or open, but this almost surely does not make a difference.) ... (more)	—	8 months ago
Answer	—	A: how to mathematically express a relationship in which a vector can be any 3D unit vector If I understand the situation correctly, the problematic issue is the zero rotation, and the issue is that if you do not rotate things at all, than that corresponds to a zero rotation around any axis. If this is true, then I could understand any of your three ideas. The third one might be marginal... (more)	—	11 months ago
Answer	—	A: How to compare lotteries, when one has highest probability of winning the jackpot, but another the highest Expected Value? To understand what is happening, consider smaller and simpler numbers. Consider a first lottery with 1/100 chance of winning 10 units, and thereby an expected value of 1/10. Then consider a second lottery with 1/1000 chance of winning 100 units. The expected value is still 1/10, even though the... (more)	—	11 months 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." One can try to make the arguments mathematically more precise. The first claim is that each patient has a 42 % chance of being cured with the treatment. The second claim is saying there is a genetic factor that 42 % of people have, such that the conditional probability of being cured given the fa... (more)	—	12 months ago
Question	—	The meaning of $\pm$ Consider the claim $ |x| = \pm x $. I would interpret it as stating that $|x| = x$ and $|x| = -x$, thereby implying that $x = 0$. A user at Matheducators stackexchange interprets it as saying that $|x| = x$ or $|x| = -x$, which holds for all real numbers. I would typically use the notation ... (more)	—	about 1 year ago
Question	—	Connection between caustics and conjugate points? Conjugate points on manifolds are, roughly speaking, points which are connected by a multitude of geodesics, so that there are problems with uniqueness of the shortest path between the points. In symplectic geometry there is the concept of caustics, https://en.wikipedia.org/wiki/Caustic(mathematic... (more)	—	about 1 year ago
Answer	—	A: Is there a way to encode a unique arrangement of vertices of a graph with a unique short word? As mentioned in a comment, you seem to wish to classify sets of points, not graphs as such. If you wish to classify them bijectively with word, you need the cardinalities of the sets to match; that is, there must be the same amount of possible word and the same about of possible sets of points. ... (more)	—	over 1 year ago
Answer	—	A: What's the common ratio for this geometric sequence? If you look at the first sequence and divide every term by 14, you get a much simpler sequence. Consider how you could find the ratio from this and try the method on the second sequence. Further solution/hint You can divide by the first term in the second sequence, too. What remains is essen... (more)	—	almost 2 years ago
Answer	—	A: What are the 2 arithmetic means of $x + y$ and $4x - 2y$? This problems seems to be missing information, or alternatively it is simple. Means here seems to be the difference between consecutive terms of an arithmetic sequence. Thus, the answer in the first exercise consists of the numbers 10+15, 10+25, 10+35, ..., 40-25, 40-15. That is, you start from th... (more)	—	almost 2 years ago
Question	—	Notation for one-sided hypothesis testing I see the following notation for one-sided hypothesis testing: $H0$: $K = 2$ $H1$: $K > 2$ I would find it more natural to write: $H0$: $K \le 2$ $H1$: $K > 2$ Assume a situation where $K$ is not, by definition, limited to equal or be higher than two. $K$ is just a dummy variable an... (more)	—	almost 2 years ago
Answer	—	A: Missing a solution: Are A and B always equal if A-B=0 One way to think about the question is that you get $$ (4x-12)(5-x) = 0. $$ A product $ab$ is zero if and only if $a = 0$ or $b = 0$. So you get either $4x=12$ or $5=x$, thus getting your two solutions. No division required. (more)	—	about 2 years ago
Answer	—	A: How can you analogize mathematical induction to dominoes falling, if some domino can fail to topple? It is an analogy and the essential point is that each step leads to the next, just like, in case of dominoes (when they work), each one topples the next. You have focused upon a case where the analogy breaks. It is a good idea to detect such cases and maybe it makes the analogy less useful for you... (more)	—	over 2 years ago
Answer	—	A: Is Mathematical Induction truly "induction", or misnamed? Mathematical induction is a case of deductive reasoning. It uses some kind of inductive principle, and the justifications for why that holds are a different matter. But its use is a case of rigorous, deductive reasoning. Finding the matter to be proved deductively is often a creative process th... (more)	—	over 2 years ago
Answer	—	A: How do mathematicians measure shape perimeters? A physical circle would be measured in centimeters or other applicable unit. A circle in a coordinate system is measured by the unit implied by the coordinate system. A circle in a more general Euclidian space is measured by building a measure, which is done by assigning length one to some line... (more)	—	over 2 years ago
Answer	—	A: How to determine area of square using Calculus in Cartesian coodinate? First, as pointed out in the comments, you have the equation for a circle there. Second, as an easy simplification, you might want to replace $\sqrt{25}$ with just a number. Third, your figure consists of pieces of lines, so we would expect to see linear equations. I would recommend checking or... (more)	—	over 2 years ago
Answer	—	A: Besides guaranteeing 0 ≤ P(A ∩ B) ≤ 1, why can't Independence be defined as P(A ∩ B) = P(A) +,-, or ÷ P(B)? 1. Try with different combinations of probabilities: what is their sum, difference, division. Not all of these are probabilities. (Check this.) This would cause a problem. 2. Draw a square; think of it as the unit square $[0, 1] \times [0, 1]$. On $x$-axis mark the (probabilities of) the events $A... (more)	—	over 2 years ago
Question	—	Questions with a quote/screenshot and a request to explain There are quite many questions that consist of a screenshot-quote, possibly several, usually with an underlined part and a request to explain it. These questions read to me as lacking effort and context. In my opinion, they would be much improved by expressing the issue in the querent's own words.... (more)	—	almost 3 years ago
Answer	—	A: Notation for Euclidean Norm Are you in a context where you use vector norms with several $p$-values? Then write them as $||x||p$. If you only use the one with $p=2$, and no other confusing notation, then it is quite safe to omit the subscript. If you instead are interested in the question of which is used more often, it i... (more)	—	almost 3 years ago
Answer	—	A: Why always rationalize a denominator? This answer is based on self-reflection, not research literature, so take it for what it is worth. Generally speaking, to understand an expression, I would prefer most mathematical objects there to be "simple": positive rather than negative, integer if possible, rational rather than a root express... (more)	—	over 3 years ago
Question	—	Title with math looks very wrong The title of the question https://math.codidact.com/questions/278141 looks very wrong to me after opening the question. It looks like the word preceding mathematics is on a lower line than previous words, and the mathematics itself is between these lines. Windows 10, Firefox. I'll see about a s... (more)	—	over 3 years ago
Question	—	The probability distribution of rolling $n$ dice and keeping $k$ highest In many roleplaying games one rolls a handful of dice and calculates their sum. In some games there are bonus or penalty dice, so that we roll, for example, 4 dice with six sides and take the sum of the three highest, ignoring the lowest. So let us fix some notation. We are rolling $n \ge 0$ dice ... (more)	—	over 3 years ago