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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
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
algebra precalculus - Zero to the zero power – is $0^0=1 . . . As for the simplified versions of the above laws, the same can be said for 00 = 0 0 0 = 0, so this cannot be a justification for defining 00 = 1 0 0 = 1 00 0 0 is ambiguous in the same way that the number x x is ambiguous in the equation 0x = 0 0 x = 0
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
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
Prove that $mn lt; 0 \iff m - Mathematics Stack Exchange Prove that mn <0 m n <0 if and only if m> 0 m> 0 and n <0 n <0 or m <0 m <0 and n> 0 n> 0 m, n m, n element of integers Just starting out teaching myself discrete math still really bad at proofs, any help advice on how to think go about this would be greatly appreciated
Definition of $L^0$ space - Mathematics Stack Exchange L0 L 0 is just a notation to refer to the weakness of the topology of convergence in measure It is not locally bounded but is metrizable if the underlying measure space is non-atomic and σ σ -finite
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