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Questions tagged [terminology]

Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

Terminology is a discipline that studies, among other things, the development of terms and their interrelationships. This tag is intended to be used for questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

8534 questions
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Difference between axioms, theorems, postulates, corollaries, and hypotheses

I've heard all these terms thrown about in proofs and in geometry, but what are the differences and relationships between them? Examples would be awesome! :)
Gordon Gustafson
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51
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What is the difference between being unique, unique up to isomorphism and unique up to unique isomorphism?

Could anyone explain the difference between the above mentioned terms "unique", "unique up to isomorphism" and "unique up to unique isomorphism", preferably with an example? Are there other characterisations of being unique "up to something"?
user91218
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What does the term "undefined" actually mean?

I have read many articles on many sites and in many books to understand what undefined means? On some sites of Maths, I read that it could be any number. and on some sites, I read that it may be some undefined thing; and there are more definitions.…
Sufyan Naeem
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How did "one-to-one" come to mean "injective"?

How did a "one-to-one" function come to mean an injective one? I find it so non-intuitive that I often have to backtrack when reading texts that use "one-to-one" because I suddenly discover that I have been internalizing it as "bijective". If there…
hmakholm left over Monica
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4 answers

What do Algebra and Calculus mean?

I sometimes see phrases like 'the relational algebra' or 'the lambda calculus'. What is the difference between an algebra and a calculus?
Scott Weinstein
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6 answers

Lemma vs. Theorem

I've been using Spivak's book for a while now and I'd like to know what is the formal difference between a Theorem and a Lemma in mathematics, since he uses the names in his book. I'd like to know a little about the ethymology but mainly about why…
Pedro
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What does "s.t." mean?

English is my second language and I have a question. What does "s.t." mean? $ \text{min} \quad f(x) = (x_1−2)^2+(x_2−1)^2 $ $ \text{s.t.}\qquad g_{1}(x) = x_{1} - 2x_{2} + 1 = 0 $ $ \qquad\qquad g_{2}(x) = \frac{x_{1}^2}{4} - x_{2}^2 + 1 \ge 0 $
Heniek Kowalski
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Difference between pairwise distinct and unique?

I've come across the term "pairwise distinct" in many research papers. But, I don't understand how it differs from just saying that the elements of a set are unique instead of saying that they are pairwise distinct. Can someone please explain the…
n1kh1lp
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What comes after length, area and volume?

The length of the unit is 1. The area of the unit square is 1. The volume of the unit cube is 1. The $\color{red}{???}$ of the unit tesseract is 1. The $\color{blue}{???}$ of the unit 5-cube is 1. So this is a fill in the blanks-question,…
Frank Vel
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When should I use "graph" vs. "plot"?

My ODEs textbook uses both graph and plot but I can't figure out how it chooses one over the other. From the book: Sketch the graph of the solution in the x1x2-plane for t ≥ 0. [this one was referring to a continuous function] Also from the…
Adam
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What is the difference between a generalization and an extension?

Generalizations and extensions are commonplace in mathematics, but I am not clear on what the difference is between the two. Are they really only synonyms? If not, I would appreciate having an example of each, with it being made clear why the…
user27325
23
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5 answers

Difference between "space" and "mathematical structure"?

I am trying to understand the difference between a "space" and a "mathematical structure". I have found the following definition for mathematical structure: A mathematical structure is a set (or sometimes several sets) with various associated…
davitenio
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Nonnegative vs non-negative

When you write about integers that are not negative, do you write "non-negative integers" or "nonnegative integers" in papers in US English? EDIT: In https://ieeecs-media.computer.org/media/conferences/cpstemplates/8.5x11x2/instruct8.5x11x2.pdf we…
user691231
22
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3 answers

What is the difference between an "empty interior" and a "hole" in topology?

I am studying an Amazonian language, Palikur, whose speakers think of objects in terms of their outside and inside. The language describes these two attributes according to their openness or compactedness, i.e. being open, or partially open, or…
Diana M Green
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Alternative ways to say "if and only if"?

There are some scenarios about which I would like to get some confirmation: when defining a concept A, We call A, if ... [definition of concept A] Does "if" here mean equivalence instead of just sufficiency? Is it incorrect to replace "if"…
Tim
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