  # kmath

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Lepton
1. Although the set of real numbers and the set of natural numbers each contain an infinite numbers of elements, the set of reals has a higher cardinality than the set naturals. Why is that?
2. I tell non-math I'm studying linear algebra and they say: "that sounds like something I took in sixth grade." So why call it linear algebra? It is supposed to be in contrast to "abstract algebra" ? Thanks
3. I need to show that $f: (0,1) \rightarrow R$ is 1-1, where $f(x)$ is given by $(2x-1)/(x^2-x)$. My attempt: suppose:$f(x) = f(y)$ Then: $(2x-1)/(x^2-x)$ = $(2y-1)/(y^2-y)$. $y(y-1)(2x-1) = (x(x-1))(2y-1)$ Reducing this leads to: $2xy^2 - y^2 + y = 2x^2 - x^2 + x$ Of course, I need to show that $x = y$ but I'm not sure how to reduce this equality any further. Any ideas? Thanks
4. How do I write matrices in latex, ie a b c d ?
5. Hello everyone, I want to make sure I understand the Cartesian product of two sets. Let A = {1, 2} B= {3, 4} Then A X B = {(1,3),(1,4),(2,3),(2,4)} Is that correct? Thanks
6. Hello everyone, For as long as I have known about the constant $e$, I have been in awe of its many uses and at times strange properties. Now I know its definition as a limit and as a series, but I have never quite understood just what makes $e$ so special, beyond the fact that it helps us solve problems. So my question is: what makes $e$ so significant to the overall study of mathematics? I hope that makes sense. I look forward to others perspective on this. Thanks
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