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Proper vector notation
I wrote a vector as $(a, b)$ in a maths exam but I was told it is not vector notation. However, I have seen this notation used all over this site and else...
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Filling a conical tank
I have been working on this problem for about 2 hours and I can't seem to get it, here is exactly what the question reads. "Water is poured into the ...
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Prove algebraically that $(\sqrt{3}+1)/(\sqrt{3}-1)=2+\sqrt{3}$
This is indeed an identity, but I cannot seem to understand how you would go about proving these two equations are equal algebraically? Do you see a metho...
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Example of a linear continuum
Definition: Let $L$ be simply ordered set with more than one element. We say that $L$ is a linear continuum iff. the following two properties holds: $L$ h...
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Fundamental group of the double torus
In May's "A Concise Course in Algebraic Topology" I am supposed to calculate the fundamental group of the double torus. Can this be done using van Ka...
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Factorial Calculation for Non-Integers?
I was playing with numbers on calculator and to my amaze i could see that calculator calculated $(4.5)!$ or any real numbers but factorial is defined for ...
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How to calculate the number of elements in all subsets of a set
There are $2^N$ subsets of a set. For instance the set $\{ 1, 2 \}$ has the following subsets: $\{ \}$ $\{ 2 \}$ $\{ 1 \}$ $\{ 1, 2 \}$ I'm trying to...
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What is the flaw in this proof that all triangles are isosceles?
What is the flaw in this "proof" that all triangles are isosceles? From the linked page: One well-known illustration of the logical fallacies to...
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Proving that orthogonal vectors are linearly independent
I am trying to prove that $a_1$, $a_2$, $a_3$ are linearly independent. I am asked to use vector product and prove that if $c_{1}a_{1} + c_{2}a_{2} + c_{3...
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The Inverse of a Fourth Order Tensor
Suppose that we have a fourth order tensor ${\bf{A}}$ $${\bf{A}}=A_{ijkl} {\bf{e}}_i \otimes {\bf{e}}_j \otimes {\bf{e}}_k \otimes {\bf{e}}_l$$ in the ort...
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