# All Questions

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### Is the set of sentences in peano arithmetic countably infinite?

Im wondering if the set of all sentences, which would be wffs in which there are no free variables, is countable infinite or not. I imagine that since the number of axioms in PA is countably ...
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Let $X$, $Y$ metric compact spaces. Prove that every continuous function $f:X\times Y\rightarrow \mathbb{R}$ is the uniform limit of functions of the form $\varphi ... 1answer 66 views ### What is the technical term for the$n$-dimensional generalization of the unit interval? What is the technical term for an$n$-dimensional generalization of the unit interval$[0, 1]$? Would we call an$n = 1,2,3,...$dimensional generalization of the unit interval an$n$-cube? 3answers 392 views ### Determinant of matrix$A^3 + 2A^2 - A - 5I$Given the eigenvalues of A So A is a 3 by 3 matrix with eigenvalues -1, 1, 2. And I have to find the determinant of $$A^3 + 2A^2 - A - 5I$$ Let$u$be the eigenvector for the eigenvalue -1. Let$S = A^3 + 2A^2 - A - 5I$then ... 1answer 74 views ###$\overline{A\cdot B}=\overline{A}\cdot\overline{B}$for$A,B\subseteq\Bbb R$? [duplicate] If$A$is a closed set in$\Bbb R$and$B$a compact set in$\Bbb R$, let$A\cdot B=\{a\cdot b:a \in A,b\in B\}$. Question: Is$\overline{A\cdot B}=\overline{A}\cdot\overline{B}$? Note: ... 1answer 131 views ### How To Simulate Mirrors/Reflection? If light is hitting a Parabolic Trough defined by$y=x^2$at a 60 degree angle from vertical so that the effective cross-section of the modified parabola is paramaterized by: x=t, y=t^2, z=tcot(60). ... 1answer 56 views ### Extraneous solutions to simple equations I had an interesting thought during my procrastination: is it legal to take an equation, say$3 = a * b * c$and do the following:$3 = abc0 = abc - 30 / a = bc - 3/a0 / b = ...
I believe I have a fundamental misunderstanding of the concept of the Vitali Covering Lemma. Definition - A closed bounded interval $[c, d]$ is said to be nondegenerate provided $c < d$. ...