# Questions tagged [terminology]

How words are used in mathematics or mathematics education

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### What is a recommend way to describe a negative number with large absolute value?

Sometimes when we discuss limits verbally, we may say that a variable $x$ being "very small" (assuming that $x$ is a real number). But this could mean any one of the following: The number $x$ is a ...
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### Metonymy in mathematics

Metonymy is a figure of speech where a word or another expression is used to mean something other than its literal meaning. This phenomenon is not restricted to the "usual human languages" (such as ...
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### Should high school teachers say “real numbers” before teaching complex numbers?

Before complex numbers are introduced in senior high school courses, should we emphasise that solutions (e.g. to quadratic equations) are real solutions? If we do, then when non-real numbers finally ...
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### Common phrases having different meaning

When talking with students it frequently happens that they misunderstand what you meant. The common example is the amount of rigor that one would consider "a proof", but there are other things, like ...
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### What is the name of the form of the line equation $y = m(x-x0)+y0$

I have been looking everywhere for the name of this form of equation of a line $y=m(x-x_0)+y_0$. It's not quite point-slope. It's the same form you would write in the linear approximation of a ...
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### Why isn't the term *inequation* widely used in English?

Just as we distinguish between an equation and an identity (or equality), why don't we distinguish between an inequation and an inequality? We solve an inequation and we prove an inequality. In French ...
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### Definition of root of equation/expression

Related: Where does the word “roots” come from when talking about zeros A student recently wrote: The positive root of 3 sin x = x is near 2. I am questioning the student's use of of the word ...
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### The word “numeral”, is it being taught and does the word exist for it in your language?

I am a mathematics educator from Lithuania and I have recently realized that there is no separate word in our language for the word "numeral". To be more precise there is no term to describe the ...
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### An alternative to “two column” geometry proofs

I'm a high school teacher in New York State (US), starting in on my first year of teaching Geometry. One of the things that really intrigues me is that the Regents exam (the state-mandated final exam)...
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### Is there a more telling name for “Calculus 2”?

I see a lot of places where "Calculus 1" is referred to as "Introduction to Calculus", or "Single-variable Calculus." "Calculus 3" is referred to as "Multiple-variable calculus." Is there an ...
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### Vocabulary for giving just numbers, not a full answer

I am a math teacher from China, teaching a course in English. Some students of mine are really good at finding answers for math problems designed in a quiz, however they are unable to write down ...
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### Interpretation of how to define “bigger” and “smaller” real numbers

This is a variant on the question small real numbers. I have a disagreement with someone about the meaning of "bigger" real numbers. Say we have the real number $-1.$ Is $0$ "bigger" or "smaller" ...
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I am reading the paper Effects of game‐based learning on students' mathematics achievement: A meta‐analysis and can't find a definition for the term "PreK‐12th‐grade students". While I know that "K-...
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### Are there textbooks that cover most etymological aspects of mathematics?

In most of the science textbooks I read, I observed that most of them contain the terms, definitions and etymology too. But nowadays, the mathematics textbooks are becoming more formal and contain ...
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### How to explain Chinese remainder theorem?

I want to explain Chinese remainder theorem to master level computer science students. There are two versions of CRT one is number theoretic and second requires the definition of ideals, groups etc. ...
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### How to verbalize the correct statement of mixed units?

I want help phrasing the instructions in a math question. The issue is the correct way to express mixed units. For example, if an answer is “25 inches,” I don’t want to accept “25 inches” or “1 foot ...
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### How to explain NP-hardness and NP-completeness to students

Computer science is becoming more and more important for mathematicians nowadays. Terms like big data, algorithm, artificial intelligence and others are frequently on the news. Many mathematical ...
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### When a geometrical figure a special case of another [closed]

Squares are special types of rectangles. Are circles special types of ellipses/ovals? Are cones special types of pyramids? I guess the answer is no because of the 2D basis: circles are not special ...
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### Should Measurement of Angles Using Degree (and perhaps Common Logarithm as well) be Avoided in Pre-Calculus?

People use degrees and radians to measure angles and though degree measurement is acceptable and is widely used in everyday life, it is not in the International System of Units and mathematically it ...
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### Proper ordering of phrase “multiplied by”

Which of these is the correct ordering: a polynomial multiplied by a monomial a monomial multiplied by a polynomial if what I want to achieve is something like 3x(x+5)? Here are my initial ...
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### “A” or “The” Cartesian plane?

Which is correct terminology: "A Cartesian plane" or "The Cartesian plane"? (As in the directions for a section of homework being, "Plot a point on ______ Cartesian plane." In that context, I feel ...
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### How to explain “fractional terms”?

as I can see there are mainly two ways to introduce fractional terms. Two examples to demonstrate the two variants: $\frac{a^2+3}{a}; \frac{3}{2c}$ $T(a) = \frac{a^2+3}{a}; T(c) = \frac{3}{2c}$. In ...
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### “The following are equivalent”

What do you say to the following way of teaching "if" and "the following are equivalent"? Has somebody ever taught it like this? An implication A -> B can be viewed as asserting that B is at least as ...
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### A good antonym for reducing/simplifying equivalent fractions

I am looking for a good antonym for reducing/simplifying equivalent fractions: 'reduce' and 'simplify' both make sense to me when dividing, but I'm struggling to name what it is we do when we multiply ...