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complex analysis - What is $0^ {i}$? - Mathematics Stack Exchange
On the other hand, 0−1 = 0 0 − 1 = 0 is clearly false (well, almost —see the discussion on goblin's answer), and 00 = 0 0 0 = 0 is questionable, so this convention could be unwise when x x is not a positive real.
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 ...
Is $0$ a natural number? - Mathematics Stack Exchange
Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was considered i...
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.
Zero power zero and $L^0$ norm - Mathematics Stack Exchange
This definition of the "0-norm" isn't very useful because (1) it doesn't satisfy the properties of a norm and (2) 00 0 0 is conventionally defined to be 1.
Seeking elegant proof why 0 divided by 0 does not equal 1
I began by assuming that 0 0 0 0 does equal 1 1 and then was eventually able to deduce that, based upon my assumption (which as we know was false) 0 = 1 0 = 1. As this is clearly false and if all the steps in my proof were logically valid, the conclusion then is that my only assumption (that 0 0 = 1 0 0 = 1) must be false.
Is $0^\\infty$ indeterminate? - Mathematics Stack Exchange
Is a constant raised to the power of infinity indeterminate? I am just curious. Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?
What is the meaning of $\\mathbb{N_0}$? - Mathematics Stack Exchange
There is no general consensus as to whether 0 0 is a natural number. So, some authors adopt different conventions to describe the set of naturals with zero or without zero. Without seeing your notes, my guess is that your professor usually does not consider 0 0 to be a natural number, and N0 N 0 is shorthand for N ∪ {0} N ∪ {0}.
A thorough explanation on why division by zero is undefined?
Getting Started The other day, I was working on a project at home in which I performed division by zero with a double precision floating point number in my code. This isn't always undefined in the computer world and can sometimes result in ∞ ∞. The reason for this is clearly explained in IEEE 754 and quite thoroughly in this Stackoverflow post: Division by zero (an operation on finite ...
How do we calculate factorials for numbers with decimal places?
I was playing with my calculator when I tried 1.5! 1.5!. It came out to be 1.32934038817 1.32934038817. Now my question is that isn't factorial for natural numbers only? Like 2! 2! is 2 × 1 2 × 1, but how do we express 1.5! 1.5! like this?
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