- I have learned that 1 0 is infinity, why isnt it minus infinity?
92 The other comments are correct: 1 0 1 0 is undefined Similarly, the limit of 1 x 1 x as x x approaches 0 0 is also undefined However, if you take the limit of 1 x 1 x as x x approaches zero from the left or from the right, you get negative and positive infinity respectively
- definition - Why is $x^0 = 1$ except when $x = 0$? - Mathematics Stack . . .
For example, 0x = 0 0 x = 0 and x0 = 1 x 0 = 1 for all positive x x, and 00 0 0 can't be consistent with both of these Another way to see that 00 0 0 can't have a reasonable definition is to look at the graph of f(x, y) =xy f (x, y) = x y which is discontinuous around (0, 0) (0, 0) No chosen value for 00 0 0 will avoid this discontinuity
- 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
- Seeking elegant proof why 0 divided by 0 does not equal 1
10 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
- 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
- How do I explain 2 to the power of zero equals 1 to a child
The exponent 0 0 provides 0 0 power (i e gives no power of transformation), so 30 3 0 gives no power of transformation to the number 1 1, so 30 = 1 3 0 = 1 Once you have the intuitive understanding, you can use the simple rules with confidence
- 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
- 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"?
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