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- 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
- 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
- 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
- What exactly does it mean that a limit is indeterminate like in 0 0?
The above picture is the full background to it It does not invoke "indeterminate forms" It does not require you to write 0 0 0 0 and then ponder what that might mean We don't divide by zero anywhere It is just the case where limx→a g(x) = 0 lim x → a g (x) = 0 is out of scope of the above theorem However, it is very common, in mathematical education, to talk about "indeterminate forms
- 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 $0^\\infty$ 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
19 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}
- 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
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