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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 $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately
- Is $0$ a natural number? - Mathematics Stack Exchange
Inclusion of $0$ in the natural numbers is a definition for them that first occurred in the 19th century The Peano Axioms for natural numbers take $0$ to be one though, so if you are working with these axioms (and a lot of natural number theory does) then you take $0$ to be a natural number
- Mathematics Stack Exchange
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- Difference between ≈, ≃, and ≅ - Mathematics Stack Exchange
For a quadratic I would set f(x) to zero but would not define f(x) as zero I use ≡ for all cases, not only immediate ones Setting f(x) to zero creates the equivalency f(x) = 0 for the coordinate you are trying to solve but is not true for all coordinates that are solvable
- What does it mean to say a divides b - Mathematics Stack Exchange
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- Normal vector to plane - Mathematics Stack Exchange
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- Improper integral of sin(x) x from zero to infinity
I was having trouble with the following integral: $\int_{0}^\infty \frac{\sin(x)}{x}dx$ My question is, how does one go about evaluating this, since its existence seems fairly intuitive, while its solution, at least to me, does not seem particularly obvious
- Example of infinite field of characteristic $p\\neq 0$
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