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- complex analysis - What is $0^ {i}$? - Mathematics Stack Exchange
0i = 0 0 i = 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x = 0 0 x = 0 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
- 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
- Seeking elegant proof why 0 divided by 0 does not equal 1
Several years ago I was bored and so for amusement I wrote out a proof that 0 0 0 0 does not equal 1 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
- Justifying why 0 0 is indeterminate and 1 0 is undefined
0 0 = x 0 0 = x 0x = 0 0 x = 0 x x can be any value, therefore 0 0 0 0 can be any value, and is indeterminate 1 0 = x 1 0 = x 0x = 1 0 x = 1 There is no such x x that satisfies the above, therefore 1 0 1 0 is undefined Is this a reasonable or naive thought process? It seems too simple to be true
- 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?
- Does negative zero exist? - Mathematics Stack Exchange
In the set of real numbers, there is no negative zero However, can you please verify if and why this is so? Is zero inherently "neutral"?
- definition - Why is $x^0 = 1$ except when $x = 0$? - Mathematics Stack . . .
But if x = 0 x = 0 then xb x b is zero and so this argument doesn't tell you anything about what you should define x0 x 0 to be A similar argument should convince you that when x x is not zero then x−a x a should be defined as 1 xa 1 x a
- Why is everything (except 0) to the power of 0 always 1?
The rule can be extended to 0 0 That is, we can define 00 = 1 0 0 = 1 and this makes the most sense in most places The one thing that needs to be understood is that xy x y is not continuous at (0, 0) (0, 0)
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