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### Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?

In the book Thomas's Calculus (11th edition) it is mentioned (Section 3.8 pg 225) that the derivative $\frac{\textrm{d}y}{\textrm{d}x}$ is not a ratio. Couldn't it be interpreted as a ratio, because ...
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### “Negative” versus “Minus”

As a math educator, do you think it is appropriate to insist that students say "negative $0.8$" and not "minus $0.8$" to denote $-0.8$? The so called "textbook answer" regarding this question reads: ...
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### Is $|1-i|$ larger than $1$?

I am confused about complex numbers. Does $1-i$ lie outside the unit circle? How do I show that this is larger than $1$ in absolute value?
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### Abusing mathematical notation, are these examples of abuse?

I have often seen notation like this: Let $f:\mathbb{R}^2 \to \mathbb{R}$ be defined by $$f(x,y)=x^2+83xy+y^7$$ How does this make any sense? If the domain is $\mathbb{R}^2$ then $f$ should be ...
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### Strangest Notation? [closed]

While this may be a fruitless pursuit of anecdotes, I still ask: what is the strangest (or most blatantly wrong (at least in the eyes of common notation)) mathematical notation you have ever seen?
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### $-1 = 0$ by integration by parts of $\tan(x)$

I had a calculus final yesterday, and in a question we had to find a primitive of $\tan(x)$ in order to solve a differential equation. A friend of mine forgot that such a primitive could easily be ...
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### Interpretation of “not equal” notation

This will be a short question. Let $x$, $y$, $z$ be three elements from any set. Is the following: $$x \ne y \ne z \tag{1}$$ Equivalent to: $$x \ne y, ~ ~ y \ne z, ~ ~ z \ne x \tag{2}$$ Or simply: ...
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### Which rule is applied to define the operator precedence for factorial

Please apologize the question, I struggled with finding a good formulation in the first place: Looking at $\binom{2n}{k}$ it is very clear that for n,k integer and n>k we can solve it by calculating: ...
Can someone verify whether my proof is logically correct? :) Proof: Assume $A\subseteq B$. Then for every element that belongs in A, such element also belongs in B. Then $A\cap B \subset A$. If $x \... 1answer 180 views ### Does$f^{-1}(Y)$make sense if$Y$is “bigger” than$X$My textbook asks me to decide whether or not this expression is true: Given the function$f: X \to Y$with$B_1 \subseteq Y $.$ f^{-1}(Y $\$ B_1) = X $\$f^{-1}(B_1) $I was confused because ... 3answers 150 views ### How does cardinality map a finite set to$(\{0\} \cup \mathbb{N})$? In reading Kevin Houston's "How to Think Like a Mathematician", there's a line stating the following: Let$X$be the set of finite sets. Then the cardinality of a set is a function on$X$, that is$|....
So I encountered this definition in Salas Hille Etgen's One and Several Variables Calculus: (This definition is for single variable case) Definition: Let $g:\Bbb R \to \Bbb R$ be a function defined ...