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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.

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Why are rings called rings?

I've done some search in Internet and other sources about this question. Why the name ring to this particular object? Just curiosity. Thanks.
leo
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In simple English, what does it mean to be transcendental?

From Wikipedia A transcendental number is a real or complex number that is not algebraic A transcendental function is an analytic function that does not satisfy a polynomial equation However these definitions are arguably rather cryptic to those…
AlanSTACK
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Do we have negative prime numbers?

Do we have negative prime numbers? $..., -7, -5, -3, -2, ...$
user103028
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What is the Riemann-Zeta function?

In laymen's terms, as much as possible: What is the Riemann-Zeta function, and why does it come up so often with relation to prime numbers?
BlueRaja - Danny Pflughoeft
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What are the differences between rings, groups, and fields?

Rings, groups, and fields all feel similar. What are the differences between them, both in definition and in how they are used?
cobbal
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What are the numbers before and after the decimal point referred to in mathematics?

Sorry for asking such a basic question - but is there an actual term for the numbers that appear before and after the decimal point? Example: 25.18 I know the 1 is in the tenths position, the 8 is in the hundredths position. are there singular…
Calvin Froedge
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What is the difference between a point and a vector?

I understand that a vector has direction and magnitude whereas a point doesn't. However, in the course notes that I am using, it is stated that a point is the same as a vector. Also, can you do cross product and dot product using two points instead…
6609081
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Is $0$ a natural number?

Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was considered in the set of natural numbers, but now it seems more…
bryn
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Why do we use the word "scalar" and not "number" in Linear Algebra?

During a year and half of studying Linear Algebra in academy, I have never questioned why we use the word "scalar" and not "number". When I started the course our professor said we would use "scalar" but he never said why. So, why do we use the word…
LiziPizi
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Why does mathematical convention deal so ineptly with multisets?

Many statements of mathematics are phrased most naturally in terms of multisets. For example: Every positive integer can be uniquely expressed as the product of a multiset of primes. But this theorem is usually phrased more clumsily, without…
MJD
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Are "if" and "iff" interchangeable in definitions?

In some books the word "if" is used in definitions and it is not clear if they actually mean "iff" (i.e "if and only if"). I'd like to know if in mathematical literature in general "if" in definitions means "iff". For example I am reading "Essential…
fiftyeight
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Why is $1$ not a prime number?

Why is $1$ not considered a prime number? Or, why is the definition of prime numbers given for integers greater than $1$?
bryn
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Why “characteristic zero” and not “infinite characteristic”?

The characteristic of a ring (with unity, say) is the smallest positive number $n$ such that $$\underbrace{1 + 1 + \cdots + 1}_{n \text{ times}} = 0,$$ provided such an $n$ exists. Otherwise, we define it to be $0$. But why characteristic zero? Why…
Srivatsan
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Is there an "inverted" dot product?

The dot product of vectors $\mathbf{a}$ and $\mathbf{b}$ is defined as: $$\mathbf{a} \cdot \mathbf{b} =\sum_{i=1}^{n}a_{i}b_{i}=a_{1}b_{1}+a_{2}b_{2}+\cdots +a_{n}b_{n}$$ What about the quantity? $$\mathbf{a} \star \mathbf{b} = \prod_{i=1}^{n}…
doc
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What does it mean to have a determinant equal to zero?

After looking in my book for a couple of hours, I'm still confused about what it means for a $(n\times n)$-matrix $A$ to have a determinant equal to zero, $\det(A)=0$. I hope someone can explain this to me in plain English.
user2171775
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