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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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231
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11 answers

In simple English, what does it mean to be transcendental in math?

From Wikipedia, we have the following definitions: 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…
AlanSTACK
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209
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7 answers

Do we have negative prime numbers?

Do we have negative prime numbers? $..., -7, -5, -3, -2, ...$
user103028
188
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10 answers

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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6 answers

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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165
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6 answers

What are the numbers before and after the decimal point referred to in mathematics?

Is there an actual term for the numbers that appear before and after the decimal point? For example: 25.18 I know the 1 is in the tenths position, the 8 is in the hundredths position but I am seeking singular terms which apply to all of the numbers…
Calvin Froedge
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164
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19 answers

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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159
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5 answers

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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151
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15 answers

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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151
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12 answers

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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148
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6 answers

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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15 answers

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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139
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10 answers

What's the difference between theorem, lemma and corollary?

Can anybody explain me what is the basic difference between theorem, lemma and corollary? We have been using it for a long time but I never paid any attention. I am just curious to know.
HPS
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136
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8 answers

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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7 answers

What is the difference between a class and a set?

I know what a set is. I have no idea what a class is. As best as I can make out, every set is also a class, but a class can be "larger" than any set (a so-called "proper class"). This obviously makes no sense whatsoever, since sets are of unlimited…
MathematicalOrchid
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