# Tagged Questions

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

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### Is there proof show that $\log x$ is undefined and make no sense at $x=0$?

I was asked by someone: why $\log x$ is undefined at $x=0$? Is there proof show that $\log x$ is undefined at $x=0$? Note(01):: log is the inverse function of the exponential function. note(02): ...
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### What is the difference between equation and formula?

Sometimes equation and formula are used interchangeably, but I was wondering if there is a difference. ...
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### The Standarization of Matrix by Vector Multiplication

I apologize for the trivialness of my question but it has been bugging me as to why the standard for multiplying a matrix by a vector that will give a column matrix mean that the vector has to be a ...
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### Is there a formal definition for antiderivatives?

In the way the derivative can be defined as a limit, specifically $$f'(x):=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ or any of the other possible variants, is there a way to define the antiderivative, as in ...
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### Question about uncorrelatedness of random variables and distributions

I was wondering, if two random variables are dependent, does that mean that they must be correlated? does one imply on the other or vice versa? Also, if I know that a joint distribution of two ...
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### Can someone explain to a calculus student what “dual space is the space of linear functions” mean?

I ran across this phrase today in a post and I am slightly confused. From my understanding, the dual space is the space of functions that sends a vector to a real number. There are two confusions: ...
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### What does “points spanned by powers” mean in the Goffinet dragon definition?

The definition of the Goffinet dragon fractal given by Wolfram Mathworld refers to plotting all points spanned by powers of the complex number p=0.65-0.3i What does it mean for points to be "...
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### What does it mean to categorify something?

What does it mean to categorify something? Is there any simple illustrative example of this process? How it is done and what is it useful for? Here is where I heard it first: "Khovanov homology is ...
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### What does this definition of $C^k$ surface mean?

Reference: Richard Millman - Elements of differential geometry I'm reading this book and there is a really wierd definition in this book: To descrive the theorem, here are some definitions in this ...
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### Understanding induced representations

Let $G$ be a group and $H$ be a subgroup. Let $\phi:H\rightarrow GL(V)$ be a representation of $H$. There are three constructions in Wikipedia, but I am not really convinced by these. My question is: ...
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### Formal definition of the function $Sin$ [closed]

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 $Sin$; ...
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### Is this task defined mathematically correctly?

I wish to make a math model for predicting users clicking on context advertising. Math definition: Let $X$ be the set of users, and $Y$ be the set of adverts. We make a mapping $F: X×Y→P$ that should ...
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### Strings in a dictionary. A partial order, strict order, and total order?

Question: The domain is the set of all words in the English language (as defined by, say, Webster's dictionary). Word $x$ is related to word $y$ if $x$ appears as a substring of y. For example, "ion" ...
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### X - Y in a finite set

Question: The domain is the power set of a finite set. $X$ is related to $Y$ if $X - Y$ is not empty. Is it a partial or strict order? If it is a partial order or strict order, is it also a total ...
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### Partial order or strict order

Question: The domain is the set of all positive integers. $a$ is related to $b$ if $b = a⋅ 3n$, for some positive integer $n$. Because of the equal sign, isn't this relation symmetric, transitive, ...
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### How to define a specific ring using a homomorphism

If we have a ring $R$ then I can form a ring of matrices isomorphic to $R$ by setting $r \overset{\phi}{\mapsto} \left( \begin{array}{ccc} r & 0 \\ 0 & 0 \end{array} \right)$ and defining ...
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When we say that two substitutions, say $\theta,\sigma$ agree on the variables of a term $t$ what exactly do we mean ? Is it that both substitution act on the same variables and substitute them with ...
I just want to know if the following are considered partially ordered sets or total set. Here is the definition: $\mathbb{R}^2$ : (a,b) R (c,d) iff $a\leqslant c$ and $b\leqslant d$ $\mathbb{R}^2$ ...