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how do I prove that $1 > 0$ in an ordered field?
I've started studying calculus. As part of studies I've encountered a question. How does one prove that $1 > 0$? I tried proving it by contra...
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How to interpret this $(\bigcap)$ mathematical symbol?
I came across this symbol $(\bigcap)$ and I do not know what it means. I have tried to check this list but I haven't gotten any clue. I am well aware...
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Product space and product topology
I have been told that (in context of Tychonoff's theorem) that $\prod_{i\in I}X_i$ (take for example $I=\{1,2\}$) and $X_1 \times X_2$ are isomorphic...
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How many integer solutions are there to the equation $x_1 + x_2 + x_3 + x_4 = 12$ with restrictions on $x_1,x_2,x_3,x_4$?
How many integer solutions are there to the equation $x_1 + x_2 + x_3 + x_4 = 12$ with $x_i > 0$ for each $i \in \{1, 2, 3, 4\}$? How many solutions wi...
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how to find the equation of a tangent line to a circle, given its slope and the eq. of the circle?
So I have a circle: $(x-2)^2 + (y-2)^2 = 25$ and I have a tangent line to this circle, with a slope of $m= -3/4$. I have to find the equation of the tange...
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How do you find the distance between two points on a parabola
So I've been wanting to figure out a formula for an odd pattern I found... but to write a proof, I need to know one thing... How do I find the distan...
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Find all roots of $\,(x + 1)(x + 2)(x + 3)^2(x + 4)(x + 5) = 360$
The question is to find all complex roots of $$(x + 1)(x + 2)(x + 3)^2(x + 4)(x + 5) = 360$$ and it is meant to be solved by hand. Is there any quick way ...
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Intuition for definition of projective module
A free module is rather intuitive: there exists a subset satisfying suitable properties which may act as a basis for elements. Taking as example an $\math...
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Knot Complement of Knot Sum and Fibered Knot Sum
Let $K_1,K_2$ be two knots and $X_1, X_2$ be their knot complements. Let $K_3$ be sum of two knots and $X_3$ the resp. complement. I am tempted to thinkin...
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What is the derivative of a function of the form $u(x)^{v(x)}$?
So I have a given lets say $(x+1)^{2x}$ in addition to $\frac{\mathrm dy}{\mathrm dx}a^u=a^u\log(a)u'$. I still have to multiply this by the derivati...
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