factorial - Why does 0! = 1? - Mathematics Stack Exchange
...Possible Duplicate: Prove 0! = 1 0! = 1 from first principles Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product of 0 and anything is 0 0, and seems like it would be reasonable to assume that 0! = 0 0! = 0. I'm perplexed as to why I have to account for this condition in my factorial function (Trying to learn ......
https://math.stackexchange.com/questions/25333/why-does-0-1
What does the notation $[0,1)$ mean? - Mathematics Stack Exchange
...16 I am studying the procedure for bucket sort from Introduction To Algorithms by Cormen et al, which assumes that the input is generated by a random process that distributes the elements uniformly and independently over the interval $ [0,1).$ What does this mean? Why there is no "]" closing bracket for the interval?...
https://math.stackexchange.com/questions/181750/what-does-the-notation-0-1-mean
algebra precalculus - Zero to the zero power ? is $0^0=1 ...
...The argument seems to hinge on whether one is to define 0^0=1 and economize several definitions and theorems from algebra, combinatorics, and analysis, at the expense of one caveat for a single function, OR to leave 0^0 undefined, have several caveats so as to preserve the continuity on the domain of definition of a single function, namely x^y....
https://math.stackexchange.com/questions/11150/zero-to-the-zero-power-is-00-1
algebra precalculus - Prove $0! = 1$ from first principles ...
...You can also prove it by moving the space: "0! = 1" ? "0 != 1", which is computer notation for "0 ? 1" :-). Then it depends on what you count as "first principles". If we're dealing with the natural numbers, this follows from the Peano axiom that the successor of a natural number is not 0 (1 being defined as the successor of 0)....
https://math.stackexchange.com/questions/20969/prove-0-1-from-first-principles
definition - Why is $x^0 = 1$ except when $x = 0$? - Mathematics Stack ...
...Why is any number (other than zero) to the power of zero equal to one? Please include in your answer an explanation of why $0^0$ should be undefined....
https://math.stackexchange.com/questions/135/why-is-x0-1-except-when-x-0
What does x ? {0, 1}* mean? - Mathematics Stack Exchange
...I was reviewing some papers and came across the notation x ? {0, 1}* I want to know what it means. Thank you! Edit: I noticed I did not put enough context to the question. The paper I reviewed was ......
https://math.stackexchange.com/questions/4231050/what-does-x-%e2%88%88-0-1-mean
Why is 0 factorial equal to 1? Is there any pure basic mathematical ...
...If you are starting from the "usual" definition of the factorial, in my opinion it is best to take the statement 0! = 1 0! = 1 as a part of the definition of the factorial function, as anything else would require proofs using the factorial to include special cases for 0! 0! and 1! 1!....
https://math.stackexchange.com/questions/4015455/why-is-0-factorial-equal-to-1-is-there-any-pure-basic-mathematical-proof
Proving $(0,1)$ and $[0,1]$ have the same cardinality
...Prove $ (0,1)$ and $ [0,1]$ have the same cardinality. I've seen questions similar to this but I'm still having trouble. I know that for $2$ sets to have the same cardinality there must exist a...
https://math.stackexchange.com/questions/1006445/proving-0-1-and-0-1-have-the-same-cardinality
What does $\ {0 , 1\}^+$ mean? - Mathematics Stack Exchange
...I am familar with what $\Sigma^*$ means, as has already been clarified in this question : What does $\ {0, 1\}^*$ mean? , however i am very puzzled by what $\Sigma^+$ refers to....
https://math.stackexchange.com/questions/3996931/what-does-0-1-mean
How to understand why $x^0 = 1$, where $x$ is any real number?
...10 There are many answers about why x0 = 1 x 0 = 1 for general x x, so I'd like to address a different issue here, the way you think about exponentiation, which seems to be troubling you. The definition you use for exponentiation holds true for integers, and rationals if you define what x1/n x 1 / n means, but what about the irrationals?...
https://math.stackexchange.com/questions/238300/how-to-understand-why-x0-1-where-x-is-any-real-number