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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
- algebra precalculus - Zero to the zero power – is $0^0=1 . . .
Whereas exponentiation by a real or complex number is a messier concept, inspired by limits and continuity So $0^0$ with a real 0 in the exponent is indeteriminate, because you get different results by taking the limit in different ways
- I have learned that 1 0 is infinity, why isnt it minus infinity?
1 x 0 = 0 Applying the above logic, 0 0 = 1 However, 2 x 0 = 0, so 0 0 must also be 2 In fact, it looks as though 0 0 could be any number! This obviously makes no sense - we say that 0 0 is "undefined" because there isn't really an answer Likewise, 1 0 is not really infinity Infinity isn't actually a number, it's more of a concept
- Mathematics Stack Exchange
How to identify process' serving 127 0 0 53:53 and 127 0 0 54:53? What is the outcome when an officer's statement under oath contradicts video evidence Advantage of launching a rocket from the Equator
- How do I explain 2 to the power of zero equals 1 to a child
If $2^0$ is any number, it makes more sense to consider that $2^0=1$ than considering $2^0$ as any other numbers (such as $0$) 2 It is more interesting to consider $2^0$ to be $1$ than giving up Some of the other answers provide good ways to convince a child of these facts
- What does it mean to have a determinant equal to zero?
The volume of the parallelepiped determined by the row vectors of the matrix is $0$ The system of homogenous linear equations represented by the matrix has a non-trivial solution The determinant of the linear transformation determined by the matrix is $0$ The free coefficient in the characteristic polynomial of the matrix is $0$
- Newest Questions - Mathematics Stack Exchange
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