dbmag9
  • Member for 8 years, 9 months
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"Modus moron" rule of inference?
12 votes

As others have said, the question is asking whether it is necessarily the case that whenever $P \Rightarrow Q$ and $Q$ are true, $P$ must be true. My personal favoured instantiations of $P$ and $Q$ ...

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Does a semicircle have 2 right angles?
7 votes

As you identify in your question, the real point of contention is the definition of angle. As the other answers have indicated, if your definition includes angles at the intersection of two curves ...

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Why are symbols not written in words?
4 votes

An important point that the other answers haven't (I believe) mentioned: for many mathematical symbols, the natural language 'word-phrase' has a subtly different meaning. A few examples: $\exists$ ...

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A dumb question on continuity and differentiability of function
Accepted answer
2 votes

The derivative $f'(0)$ is defined by $$\lim_{h\to 0} \frac{f(0+h)- f(0)}{h}$$ so you are evaluating $f$ at $x$-values other than $c$. So the question comes down to whether the values of $\frac{f(0+h)-...

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Does the definition of a bijection and surjection not depend on our definition of the range?
Accepted answer
2 votes

What you are calling the range would more commonly be called the codomain of the function (the range is then defined as the image of the domain, i.e. for $f:A\to B$, the set $\{f(x) : x\in A\}$. With ...

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Set Description and their Context (Context of a Set)
Accepted answer
2 votes

If you want to distinguish between a set of numbers and a set of representations of numbers, the most obvious thing would be to describe the set as a subset of some well-understood (or at least better-...

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Introductory books on complex analysis?
2 votes

Should throw my mortarboard into the ring and plug Hilary Priestley's Introduction to Complex Analysis. I'm certainly finding it useful.

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Equivalence Relations lists
0 votes

Your suggested answer is incorrect. Your condition states that every $x\in X$ must appear the same number of times in the first list as it does in the second. So if $(a,b,c)\sim (0,1,2)$ then $(a,b,...

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Is this logic proof correct?
0 votes

Your attempt does not make sense. The biggest problem is your misunderstanding of how the quantifiers work. Expressions like '$\forall x \in \mathbb Z$' and $'\exists x \in \mathbb N$' are not ...

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Well-ordered sets
0 votes

Here's a starting point: Take the well-ordering $\preceq$ on $\mathbb N$ defined by $a\preceq b \text{ if } \begin{cases}\text{$a$ is even and $b$ is odd}\\a\leq b \text{ where $a$ and $b$ both odd}...

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Prove consecutive terms in a geometric sequence and consecutive terms in an arithmetic sequence.
0 votes

Another method, which is no easier than Ángel Mario Gallegos's answer but in another case might well be more elegant: Make the same starting observations as in his: Since $a$, $b$, $c$ are ...

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