# Tagged Questions

For questions about the formulation of a proof, not about the mathematics behind it.

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### Lebesgue outer Measure of a face of rectangle in $\Bbb R^{n}$

Show that the outer measure of a face $I_1 \times \dots \times I_{i-1} \times \{a\} \times I_{i+1} \times \dots \times I_n$ of a rectangle $I_1 \times \dots \times I_n \subset \Bbb R^{n}$ is zero. ...
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### In a math paper, what is a remark?

I sometimes see paragraphs labeled 'Remark.' However, papers that include remarks also include unlabeled explanatory paragraphs (i.e. all the other writing in the article) that seem to be remarks. ...
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### If $x$ and $y$ are irrational but $x + y$ is rational then $x - y$ is irrational [closed]

Prove that if $x$ and $y$ are irrational but $x + y$ is rational then $x - y$ is irrational. I can understand how it works in my head, I don't know how to prove it though.
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### Boolean algebra proof - I don't know why this is valid!

So this is the answer proof I was given, I'm stumped by the final application of the Idempotent law (where does that 1 come from!?) As I understood it a 0 or 1 can only come from a combination of A ...
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### Show any open interval is a half open set?

How do I show that any open interval is an half open set and use this to conclude that any open set is also half open? I am in an introduction to proofs writing class. I have a feeling I need to use ...
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### Prove that $X\triangle\emptyset=X$

I'm working on my proofs involving sets, though this one is not a homework problem, so if you wish to provide your own example, so be it. I am working on exercise 3.3.14 (1) in Bloch's Proofs and ...
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### differentiable on $\Bbb R^{n}× \Bbb R^{n}$

Let $f : \Bbb R^{n} × \Bbb R^{n} → \Bbb R$ be defined by $f(x, y) = x·y$ , Show that $f$ is differentiable on $\Bbb R^{n}× \Bbb R^{n}$ and that $Df(a, b)(x, y) =b · x + a · y$ Here . denotes the dot ...
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### Finite Sets Proof on Domains [duplicate]

Just wanted some help with this little proof.: Let X and Y be Finite Sets. Prove that |X^Y| = |X|^|Y|