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Questions tagged [definition]

For requesting, clarifying, and comparing definitions of mathematical terms.

Definitions are at the core of mathematical precision; they answer the question "What is X?" in mathematics. Into this category fit questions regarding equivalence of definitions, clarification of complicated definitions, or proposed new definitions for mathematical notions, with requests for improvements or comments.

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Exponentiation with rationals - why algebraic?

Why is exponentiation with rational numbers considered an algebraic operation? I get why exponentiation with integers is since that's just a finite number of applications of multiplication, but this doesn't extend to roots.
G. Bach
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Definition of "in terms of" for a constant vs a variable

Say I have a question that says: "answer the question in terms of x" where x is a variable. vs. "answer the questions in terms of n" where n is any constant. What is the difference between the two? ( in terms of definition ) Edit: To try and…
user258218
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What to $t\wedge s$ mean when $t$ and $s$ are just scalars?

In my experience $\wedge$ has something to do with the outer product, but I am not sure what it means when $t$ and $s$ are not vectors and the book I am reading does not explain it. I thought maybe it means $min\{s,t\}$ but before the book used it…
MathStudent
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What is the corresponding term for center of mass for a two-dimensional shape?

What is the term for the point on closed surface with no holes which would correspond to the point on that surface directly above the center of mass for a 3-dimensional figure of constant density and constant thickness projected outward at 90…
WilliamKF
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Formal definition of the function $Sin$

Which is the formal definition of the function $Sin$, starting from axioms of real numbers ? I never found it in any book. Not its Taylor serie, that is based upon the intuitive definition of $Sin$; I want the formal definition of $Sin$ without…
halfpog
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Definition of Cofinal Segment

Recently I encountered the term 'cofinal segment' in the paper 'The Point of Continuity Property, Neighbourhood Assignments and Filter Convergences' by Ahmed Bouziad, example $2.3$. Question: What is the definition of cofinal segment? If possible,…
Idonknow
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How to interpret the definition of inductive set?

I can't understand the sentence below: "A subset Y ⊂ X will be called inductive if, for every x ∈ X such that y ∈ Y for all y ∈ X such that y < x, we have x ∈ Y." please tell me what's the meaning, thanks!
Song Wang
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Pairwise non-integral numbers

I have a set of complex numbers a_1 through a_n which are said to be "pairwise non-integral numbers". Could someone explain to me exactly what this means? Thanks. From comment below: I should also say the exact wording is "Pairwise different…
Set
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Trigonometry is to triangle as _____ is to circle.

What is the most suitable word to put in that gap? Something that corresponds to the study of circles.
Ogen
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Does the word scalar still apply if it's not a vector?

If I take the value of something, say $50$g and I multiply that value by something else, so perhaps $50\text{g} \times 3$ what would that $3$ be called? It acts like a scalar but I'm not sure that definition applies when we're not talking about…
user11406
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Definition: Equipollent

Does the term Equipollent simply mean bijective? I have seen that by definition a mapping is equipollent iff it is bijective. What is the point of such a statement? Context: It will be used in Zorichs's Mathematical Analysis I to define cardinality…
user142198
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Why does $0/0$ have to be undefined?

Why can't it no be $\pm$ Infinity? If $x/1$ is $x$ then $x/0$ should be $\pm$ Infinity.
user41758
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Is there any other definition of $\omega$ other than complex cube root of unity?

As far as I have learnt at the school level the meaning of $\omega$ is the complex cube root of unity that is ($\omega$)³=1, i.e. ($\omega$-1)[($\omega$)²+$\omega$+1]=0. But are there any other definitions of $\omega$ possible in mathematics? Please…
Shivam Kumar
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is x/x a proper or improper fraction?

If the numerator is greater than the denominator, it's improper. The other way around, it's proper. What if the numerator is the same as the denominator?
Alec
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Why call on an onto function surjective?

Why call on an onto function surjective?
Jared
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