Closure of the union = Union of closures
updates

Closure of the union = Union of closures

I have seen that $\text{cl}(A\cup B)=\text{cl}(A)\cup \text{cl}(B)$. However I don't see why this is true. I can see the the right to left inclusion,...

Published: Aug 22, 2026

The sum of two odd numbers is even
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The sum of two odd numbers is even

I know formal ways of proving this, but I am doing research on how middle grade students create arguments to support conjectures. I would like to anticipa...

Published: Aug 22, 2026

Calculate flux through a surface
general

Calculate flux through a surface

Part of the surface, S, is: $z=x^2+y^2$ above the disk $ \ x^2+y^2 = 1 \ $ oriented in the $\vec k$ direction. I need to set up an integrated integral to ...

Published: Aug 22, 2026

Need help visualizing the combinatorics sum & product Rule
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Need help visualizing the combinatorics sum & product Rule

I'm working on some assignments in my discrete math class for the sum & product combinatorics rules and I'm having trouble understanding the...

Published: Aug 22, 2026

Is the point at $(0,0)$ of the graph $z=x^3 + y^3$ considered a saddle point?
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Is the point at $(0,0)$ of the graph $z=x^3 + y^3$ considered a saddle point?

Is the point at $(0,0)$ of the graph $z=x^3 + y^3$ considered a saddle point? I was given that function, and I used the second-order derivative test only ...

Published: Aug 22, 2026

Monic polynomials clarification
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Monic polynomials clarification

So I know a monic polynomial is one where the coefficient of the leading term is 1, but does that mean the constant 1 is a monic polynomial too? Thanks.

Published: Aug 22, 2026

Drawing Vector Fields (beginner)
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Drawing Vector Fields (beginner)

I have $f(x,y) = xy$ which has the Gradient Vector Field F$(x,y) = (y,x)$ I believe the correct way to draw individual vectors is to map points into the f...

Published: Aug 22, 2026

Difference in meaning between converges against and converge to
general

Difference in meaning between converges against and converge to

Might be a silly question, but is there any difference between saying that a something (limit, series and so on) converges to a value and converges agains...

Published: Aug 22, 2026

What is the notation for the empty matrix?
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What is the notation for the empty matrix?

My question: What is a notation for an empty 0x0 matrix (i.e. the matrix for the only linear map $f:\{0\}\to\{0\}$)? Is it written $()$? How can I disting...

Published: Aug 22, 2026

how to find tangent line at a given point, without equation
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how to find tangent line at a given point, without equation

Find the equation of the line that is tangent to the curve at the point $(0,\sqrt{\frac{\pi}{2}})$. Given your answer in slope-intercept form. I don'...

Published: Aug 22, 2026

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