# Questions tagged [terminology]

How words are used in mathematics or mathematics education

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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.&...
1 vote
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### 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 ...
1 vote
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### 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 ...
1 vote
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### 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 ...
116 views

### 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 ...
1 vote
285 views

### 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 ...
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### 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, ...
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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 ... 123 views

### 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 ...
172 views

### 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 ...
193 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?
1 vote
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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 ...
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### 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 ...
159 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 ...
508 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 ...
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### 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 ...
195 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 ...
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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. ...
209 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 ...
4k views

### 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" ...
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### 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 (...
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### 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" ...
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### 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" ... 250 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?...
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### 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 ...
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### 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,...
1 vote
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### 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) ...
229 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 ...
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### 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 ...
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### 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 ...
179 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 ...
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### 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 ...
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### 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 ...
4k 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 ...
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### 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 ...
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 ...
1k views

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 $... 5 votes 2 answers 249 views ### Term for candidates for inflection points The critical points of a function$f(x)$are candidates for local extrema, i.e., if a function changes from increasing to decreasing, or vice versa, it must happen at a critical point. Is there an ... 9 votes 3 answers 2k views ### Definition of Trapezoid From one textbook we use in our High School - Transcription: A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid. And from ... 10 votes 2 answers 458 views ### Weekly quizzes as an alternative for midterms? What is this called? I have seen (by some of my former instructors) the following strategy applied as an alternative to traditional "midterms and final" assessment in a math course: Students take a quiz weekly. ... 9 votes 5 answers 2k views ### Is there a name for paths that follow gridlines? I'm writing up an activity where students are looking at pathlengths that follow along gridlines. Is there a word or phrase that is commonly used to describe those paths, but doesn't include ... 13 votes 7 answers 12k views ### Why don’t American school textbooks recognize negative numbers as whole numbers? Looking up for definition for whole numbers on Google yields a result which mentions: The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included). I ... 18 votes 4 answers 3k views ### Does this property of subtraction and division have a name? Addition and multiplication are commutative. Denoting$\circ$as either such operation, we have $$x \circ y = z \Leftrightarrow y \circ x = z.$$ Subtraction and division have a similar property, where ... 2 votes 1 answer 765 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$... 1 vote
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### 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 ...
583 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 ...