In category theory, an abstract branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X.
The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.
If an object is both initial and terminal, it is called a zero object or null object. A pointed category is one with a zero object.
A strict initial object I...
I'd appreciate help with solving this convex quadrilateral riddle. It appears to hold true in all of my test cases, but I'm not sure how I would go about writing a proof for it.
Let $UVWX$ be a convex quadrilateral.
Let $Y$ be the midpoint of $UX$,
and let $Z$ be the midpoint of $VY$.
...
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I am trying to integrate this expression which came up in a derivation of the momentum distribution function for an ideal gas. $\Theta(x)$ is the Heaviside step function which is $1$ when $x$ is positive and $0$ if negative.
$$\prod_{i=k+1}^{kN} \left(\int_{-\infty}^{\infty}dp_i\right)\times\...
