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factorial - Why does 0! = 1? - Mathematics Stack Exchange
$\begingroup$ The theorem that $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ already assumes $0!$ is defined to be $1$. Otherwise this would be restricted to $0

I have learned that 1/0 is infinity, why isn't it minus infinity?
As far as I am aware, when doing floating point math on most computers in most computer languages, 1.0/0.0 will yield positive infinity (-1.0/0.0 yielding negative infinity). I think this question is extremely dependent on context and usage.

Does $0 - x < 0$ imply $x =0$? - Mathematics Stack Exchange
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

What is 0 raised to 0 - Mathematics Stack Exchange
Thus, if we define $0^0$ to either $0$ or $1$ then we get problems with these functions not being continous (without jumps if you plot them) where they are defined, which is why we keep $0^0$ undefined in most cases.

Is $0$ a natural number? - Mathematics Stack Exchange
Pros of considering $0$ not to be a natural number: generally speaking $0$ is not natural at all. It is special in so many respects; people naturally start counting from $1$; the harmonic sequence $1/n$ is defined for any natural number n; the $1$ st number is $1$; in making limits, $0$ plays a role which is symmetric to $\infty$, and the ...

Finding points of a function's graph that are closest to a given point
This is a classic optimization problem where you are trying to minimize the distance from the point $(0, 2 ...

What is $P(X > 0 \mid X + Y - Mathematics Stack Exchange
X and Y are N(0,1) with correlation 0.5, what is the probability that X+Y is greater than a number Hot Network Questions Could a jet engine generate electricity for a propellor?

If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If ...
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Show that $L^p$ "space" for $0
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Prove that if $f(x) = \\int_{0}^x f(t)\\,dt$, then $f(x) = 0$
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

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