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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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Why is a sphere in an $n $-dimensional space called $(n-1) $-sphere?

Why is a sphere in an $n $-dimensional space called $(n-1) $-sphere? Isn't it natural to call a sphere in 3D a 3-sphere, a sphere in 2D (i.e. a circle) a 2-sphere, etc?
user132181
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Is "converges at" idiomatic English in some regions?

Some students write, e.g., "$\sum(1/n^2)$ converges at $\pi^2/6$", where I would write "converges to". Are there regions of the English-speaking world where it is standard to say "converges at"? Or should this be considered a mistake made by…
idmercer
  • 2,521
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Is there a name for functions that are their own inverses

There are terms for various kinds of functions (or operators) such as... associative - (a # b) # c = a # (b # c) commutative - a # b = b # a idempotent - f (f (x)) = f (x) Is there a similar name for functions that are their own inverse? f (f…
user510
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0 answers

Is there a name for this property of binary operations?

Suppose we have a set $S$ with a binary operation $*$ such that for all $x,y,z$ $\in$ $S$, $(x*y)*z=(x*z)*y$. For example, subtraction on the integers and also the real numbers has this property. Is there a standard name for this property in the…
user107952
  • 20,508
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2 answers

Does "classification" of mathematical objects have a precise meaning?

I've heard about things in math that have been "completely classified," like finite simple groups, and other things that are not completely classified, like topological spaces. Does "classification" in this sense have a generally accepted and…
WillG
  • 6,585
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Is there a name for the operands of union and intersection?

For subtraction, in $a - b$, we call $a$ the minuend and $b$ the subtrahend. With logical conjunction, $p \wedge q$, we can call $p$ and $q$ the conjuncts. Are there terms like this for the operands of set union? Is there a term for $P$ and $Q$ in…
sgf
  • 171
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What is this property called?

Let $(V,\,+,\,\cdot\,)$ be a vectorspace and $D\subset V$ a set with the following properties For $\;\lambda D:=\{\lambda d\mid d\in D\}\;\textrm{ and}\;\;\lambda,\, \mu\ge0$: $$0\in D$$ $$\bigcup_{\lambda\in\mathbb{R}}\lambda…
CBenni
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Why is -10 smaller than -100?

My physics teacher told me recently that -10 is less than -100. The way I look at it is in 2 ways: Having minus £100 would mean you have less money that if you had -£10. If you are presented with a number spectrum ranging from -100 to 100, it is…
ODP
  • 864
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How do you call the relation between these 2 variables?

Let's say I have an X number and I want to increment it by 50%, I would get $X*A=Y$ Then in order to multiply Y and get X again I would need to do $Y*Z=X$ How do you call the relation between A and Z? Example with…
Fraaaan
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1 answer

Is there a term for a function where equal output values must come from only one contiguous range of input values?

I'm looking for a word to describe a function where every output is guaranteed to have come from exactly one contiguous range of input values. For example, a monotonic function has this property, but that is too strong: the relative ordering is…
lemnar
  • 161
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The meaning of "In general" in mathematics

What is the meaning of "in general" in mathematical texts? Does it mean usually or it means always or sometimes usually and sometimes always according to the text?
Dante
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1 answer

What do "canonical" and "natural" mean exactly?

"Canonical" and "natural" are two words frequently seen in mathematical literature. For example, we often find "there is no canonical/natural way to", "it's canonical/natural to". So I'd like to know what is exactly "canonical/natural" way and also…
zhangwfjh
  • 1,665
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existence = well-defined?

When something (like a limit) is said to "exist" is this perfectly equivalent to "is well-defined"? And, is "well-defined" more-or-less equivalent to, "computers could use this definition and there would (theoretically) be no miscommunications"?
hefalump
  • 305
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Usage of "commute"/"commutative"

I have a very elementary terminology question: When you say "$x$ and $y$ commute under some operation", can you only say that if the operation is generally commutative, or is it also used to mean that it just happens to be commutative for $x$ and…
Jason C
  • 210
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Meaning of justify

When being asked to justify some conclusion, is it same as to prove it? My memory tells me that "justify" has been used to describe some informal verification, not necessarily formal proof. I wonder if it is true? If yes, in what sense is "justify"…
Tim
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