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Questions tagged [terminology]

How words are used in mathematics or mathematics education

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"Pure Imaginary" or "Purely Imaginary"?

Quick Question: A complex number $z$ with real part $Re(z) = 0$, i.e. something like $-17i$ -- would you call it "pure imaginary", or "purely imaginary"? I'm not a native English ...
Torsten Schoeneberg's user avatar
11 votes
2 answers
916 views

What is the terminology for "self-referral" integrals in calculus?

In the topic of integration and anti-derivatives in Calculus we come across cases where the attempt at integration by parts brings us back to the original integral, the most basic example being $\int ...
Maesumi's user avatar
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5 votes
4 answers
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Educational resources commonly address slant asymptotes. Why not general polynomial asymptotes?

Back in 2018, I wrote a post about asymptotes of rational functions in which I addressed not only horizontal and slant/oblique asymptotes, but also the general case of "polynomial asymptotes.&...
Justin Skycak's user avatar
1 vote
1 answer
131 views

Idea of using LLMs to help communicate ideas in math

What do you guys think about the ideas presented in this short text: https://github.com/yougetyourmanwww/AI-for-math/blob/main/AI.md The text is about how LLMs like chatGPT can be used for when doing ...
user23248's user avatar
1 vote
2 answers
537 views

How should an educator answer a student who asks "Can this theorem be deduced in other systems of set theory?"

If the educator decides to handle the situation by declaring that the question is beyond the scope of the course, then would it be fair to ensure that the course description and course syllabus ...
ELM's user avatar
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1 vote
4 answers
217 views

Naming the procedure of converting the place values of digits

Let's say I have the numeral 2.263,3 thousands, and convert it to 2.263.300 units. How do we describe what I have done to the numeral regarding units ? I know it has to do with the place values of the ...
GJC's user avatar
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-5 votes
1 answer
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Does the "Middle School Mathematics domains" refer to (I) through (V) topics?

Does the "Middle School Mathematics domains" on page 3 of https://www.ets.org/content/dam/ets-org/pdfs/praxis/5164.pdf refer to the the following 5 topics/categories? (I) Numbers and ...
JJJohn's user avatar
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1 vote
3 answers
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Is it correct to state that a cone has no faces?

Faces are attributes of polyhedra, so it doesn't make sense to ask how many faces a cone has. Are there traditional scholars that use faces attached to cones? How do different countries deal with the ...
Humberto José Bortolossi's user avatar
7 votes
3 answers
2k views

What's it called when multiple concepts are combined into a single problem?

A lot of students complain about "never being shown that before". What's the idea called when you test multiple concepts or one or two new ones along with some old ones in a word problem, ...
E2R0NS's user avatar
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1 answer
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‘Induction on’ vs ‘Induction with respect to’ in math

I heard one mathematician who said “induction on 𝑛” and another who said “induction with respect to 𝑛”. Do these two expressions mean exactly the same thing mathematically? If so, then are they ...
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3 votes
0 answers
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congruency: how widely used?

Today I was made aware of the term "congruency" as a word related to congruence in the same way that equality is related to equation. I have never seen the term "congruency" used ...
KCd's user avatar
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1 vote
1 answer
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Importance of etymological approach to terminology

Here I have two issues related to this post. How can etymological approach to a language be used to improve creativity skills of mathematics in students; I think, knowing the evolution which has ...
Janaka Rodrigo's user avatar
2 votes
1 answer
213 views

What is the terminology for integers with the same oddness or evenness?

If two integers are either both negative or both positive, we can say they have the same sign. How about two integers that are either both odd or both even? Is there any term for them?
D G's user avatar
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1 vote
1 answer
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Triples or triplets in Pythagoras theorem

We usually say (3,4,5) , (5,12,13) as Pythagorean triples. What is much better way to refer those sets of numbers, Pythagorean triples or Pythagorean triplets? According to the normal usage we say ...
Janaka Rodrigo's user avatar
8 votes
5 answers
894 views

What should I call the "important" values of x?

When analyzing the functions $f(x) = \sqrt{x-5}$ $g(x) = \frac{1}{x-5}$ $h(x) = 2^{x-5}$ we know that it is useful to think about what happens at $x = 5$. For the function $f$, this logic will ...
Chris Cunningham's user avatar
3 votes
2 answers
161 views

Word for an object being extended: Given F, a function that extends F is called an extension and F is called the extension __?

If a field L extends a subfield K then L is called an extension of K and K is called the extension's base field. See extension field for a definition. What is the analog of "base field" when ...
mgkrupa's user avatar
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3 votes
5 answers
537 views

Why do we explicitly state the equality of two things when we know they're equal

Recently my brother in high school and I were talking about some math when he said If we know two things are the same i.e. equal why do we need to state that they're the same? What he was trying to ...
Harshit Rajput's user avatar
21 votes
7 answers
2k views

Is there a canonical name for a polynomial-like expression allowing for negative powers?

When introducing the techniques of differentiation, polynomials come up all the time as great examples to familiarize students with the "power rule" and the linearity of differentiation. A ...
Kelvin Soh's user avatar
4 votes
1 answer
208 views

Why is there variation in the meaning of "Standard form" for a quadratic?

I'm teaching this year out of "Precalculus with limits" by Ron Larson [7th ed], and the following expression appears in the unit introducing polynomial functions: $f(x)=a{(x-h)}^2+k$ He ...
Cassius12's user avatar
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5 votes
4 answers
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what could be some replacement language for the term "spoon feeding"

In some cultures, there is an expression of "spoon feeding" type of instruction, where the teacher shows how to do steps to a problem, and then students are assigned minor variants thereof. ...
usr0192's user avatar
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2 votes
2 answers
266 views

Is coefficient same as constant?

I was studying about polynomials when I stumbled upon this video https://www.youtube.com/watch?v=vBfdYuoc3x4&list=PLjS5lmipV2HJEaKfdeVSKdprfFxinzmNw&index=2 The video says that a monomial has ...
Noob_Guy's user avatar
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30 votes
12 answers
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How can I validate the existence of percentages above 100?

I once encountered a math educator whose personal pet peeve was the "give 110%" meme. He drilled into his students that 100% was the literal maximum. Percent came from "per cent" ...
rprospero's user avatar
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5 votes
1 answer
553 views

Definition for Mathematical Formula

Imagine that you were writing an elementary book, for example for high school learners, and at the beginning you had a glossary where you wanted to write the definitions for common mathematical words (...
fire-bee's user avatar
  • 173
5 votes
2 answers
971 views

Is "Annular Ring" redundant?

I've come across the term annular ring in parentheses following washer in my calculus textbook: "has the shape of a washer (an annular ring)". The definition of the word "annular" ...
Brian's user avatar
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3 votes
5 answers
2k views

What term describes the relationship between tenth, hundredth, thousandth and the number ten?

What term describes the relationship between tenth, hundredth, thousandth, et cetera (1/10, 1/100, 1/1000, ...) and the number ten? (Despite what some may say, I don't accept that "decimal" ...
user avatar
0 votes
1 answer
268 views

Why do so many children's book confuse discs with circles? [duplicate]

The difference between a disc (disk) and a circle is crystal clear to me: However, in many children's books, a disc is usually called a circle: Why do many children's book confuse discs with circles?...
Zuriel's user avatar
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13 votes
5 answers
2k views

Use of language: "perfect square". is this useful or a hindrance? [closed]

I have recently been noticing the tendency to use the term "perfect square" when "square number" is really what is meant. Usually I have seen it at elementary level: introductory ...
Prime Mover's user avatar
4 votes
1 answer
178 views

Are ‘constant difference’ and ‘common difference’ synonymous?

I’ve seen at least two phrases to describe a fixed difference between two numbers, i.e., “constant difference” and “common difference.” For example, if Sibling A is 10 years older than Sibling B today,...
EJ Mak's user avatar
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1 vote
2 answers
6k views

Is there a difference between 'subtract' and 'subtract by'?

A basic terminology question for a foreign speaker. Please correct me if wrong. (Let's ignore the commutative property of + and * here) ...
jf328's user avatar
  • 129
-4 votes
1 answer
238 views

Can you talk about (the rest of the) field axioms when the operations are not closed? [closed]

Note: Updated based on this. In my course, my instructor posed the following exercise: Let $S$ be the subset of $\mathbb R^n$, $S=\{(a_1,a_2,a_3...a_n) | a_2 = \pm a_1, a_3=...=a_n=0 \}$. Define ...
BCLC's user avatar
  • 574
6 votes
2 answers
336 views

Is there an equivalent for "tiervenner" in English or other languages?

In Norway a widely used concept is that of "tiervenner", "ten friends" (my translation to Finnish is "kymppikaverit"). This simply means numbers (implicitly positive ...
Tommi's user avatar
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5 votes
4 answers
2k views

Composite fraction?

What do you call a fraction that has one fraction in the numerator and also one in the denominator? I mean (a/b)/(c/d). The word by word translation from my native language would be: composite ...
Jan's user avatar
  • 51
-4 votes
1 answer
180 views

Is there an **official** name for the following "digit reduction" operation? [closed]

In one of my programs I have a function I call reduce(n) which associates to n the recursive sum of ...
mszmurlo's user avatar
  • 135
4 votes
3 answers
526 views

What is the English word for the French "repère"?

I'm preparing a holiday class in computer graphics. The class will be held in English. I'm a French speaker and I'm fighting with some words which have lots of meanings to find the right one in the ...
mszmurlo's user avatar
  • 135
-2 votes
3 answers
195 views

A linear equation -- my approach

Here is an example of a lesson I did on linear equations where my objective was to show that they are equations of first degree. The reason I do it this way is because I tend to find that students ...
Wasp's user avatar
  • 187
24 votes
9 answers
5k views

Why do we introduce the notion that triangles are "congruent" instead of just saying that they are "the same" or "equal"?

The assumed age of the students is 10-15 years old. What is the danger in saying that two triangles are "the same" or "equal" instead of saying that they are congruent? It seems to ...
Improve's user avatar
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17 votes
12 answers
7k views

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

The imagined students are in elementary school, say around 9-13 years old. I want to use rather precise terminology when talking to my students. However, it seems like we typically use the same ...
Improve's user avatar
  • 1,881
3 votes
1 answer
74 views

simple statistics (binomial) terminology

Say I have the problem: I roll a die three times and I am interested in the probability of ending up with two 1's. My impression is that a single roll is called a trial. What is the full 3-roll action ...
Nights's user avatar
  • 183
14 votes
5 answers
1k views

Is "conjugate of a binomial" a standard terminology?

In several online high school teaching resources (I do not want to single out any) I see that $a-b$ is referred to as the conjugate of $a+b$ with no restriction on $a$ and $b$. I can understand that $...
Ferenc Beleznay's user avatar
5 votes
2 answers
254 views

Term for candidates for inflection points

The critical points of a function $f(x)$ are candidates for local extrema, i.e., if a function changes from increasing to decreasing, or vice versa, it must happen at a critical point. Is there an ...
Jared's user avatar
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9 votes
3 answers
2k views

Definition of Trapezoid

From one textbook we use in our High School - Transcription: A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid. And from ...
JTP - Apologise to Monica's user avatar
10 votes
2 answers
478 views

Weekly quizzes as an alternative for midterms? What is this called?

I have seen (by some of my former instructors) the following strategy applied as an alternative to traditional "midterms and final" assessment in a math course: Students take a quiz weekly. ...
Opal E's user avatar
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9 votes
5 answers
2k views

Is there a name for paths that follow gridlines?

I'm writing up an activity where students are looking at pathlengths that follow along gridlines. Is there a word or phrase that is commonly used to describe those paths, but doesn't include ...
David Elm's user avatar
  • 485
13 votes
7 answers
12k views

Why don’t American school textbooks recognize negative numbers as whole numbers?

Looking up for definition for whole numbers on Google yields a result which mentions: The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included). I ...
codespeare's user avatar
18 votes
4 answers
3k views

Does this property of subtraction and division have a name?

Addition and multiplication are commutative. Denoting $\circ$ as either such operation, we have $$x \circ y = z \Leftrightarrow y \circ x = z.$$ Subtraction and division have a similar property, where ...
Reinstate Monica's user avatar
2 votes
1 answer
889 views

In single variable calculus, do you distinguish between critical and singular points?

In some texts, a critical point is when the derivative exists and is zero, and a singular point is when the derivative does not exist. So I suppose, at $x=0$, $|x|$ would have a singular point while $...
user avatar
1 vote
1 answer
240 views

What to call a symbol that denotes an "undisclosed" given number? [closed]

Students like to categorize notations to pin down their understanding of exactly what these notations stand for. Thus, given the expressions $f(x_{0})=f(x)|_{x\leftarrow x_{0}}$, $x=x_0+h$, or $lim_{x\...
schremmer's user avatar
  • 864
11 votes
2 answers
325 views

Confusing verbal descriptions of function transformations

While teaching Function Transformations, I found the verbal descriptions of stretch and squeeze really confusing. So for $y = f(x)$, $y = 2f(x)$ is said to stretch $f(x)$ vertically by a factor of $...
reflectionalist's user avatar
32 votes
6 answers
3k views

Allowing nonstandard mathematical language and/or notation

How important is enforcing standard mathematical language and/or notation? Today, I was questioned by a writing instructor as to how vital it is to correct students when they explain something using ...
Nick C's user avatar
  • 9,639
11 votes
3 answers
640 views

Terminology for parts of limit notation

When we talk about: $$\lim_{x\to{c}}f(x)=L.$$ Is there a formal name for the number "$c$"? I know that the notation means "$L$ is the limit of $f(x)$ as $x$ approaches $c$". It ...
Ari's user avatar
  • 379