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Original post by Aph
is that an emoticon?
Original post by flou_fboco2
is that an emoticon?
Nooo...
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Original post by Aph
[scrollr]
[/scrollr]Original post by Aph
it doenst scare me
Original post by Aph
What makes you think that it scares anyone?
Original post by TenOfThem
What makes you think that it scares anyone?
Because many people deny its existence
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G-g-g-get it away
But seriously, I don't know
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But seriously, I don't know
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Original post by Aph
Because many people deny its existence
Really
Are you sure they do not just believe that it is "undefined"
Original post by TenOfThem
Really
Are you sure they do not just believe that it is "undefined"
Are you sure they do not just believe that it is "undefined"
Well maybe but its obvious that it is equal to infinity
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Original post by Aph
Isn't it 1?
Haven't done Maths for ages...
Original post by Aph
hmmmm
Original post by Aph
We can easily show the limit of x^x as x approaches 0 is 1.
So why has it scared you?
Original post by newblood
Doesnt scare me nor anyone. Simple limits.
0^0=1
0^0=1
Not as simple as you think. If exists then . This is obviously not true for all paths to in .
Original post by newblood
We can easily show the limit of x^x as x approaches 0 is 1.
So why has it scared you?
So why has it scared you?
Ok but surely it equals all numbers
It hasn't though the weird things thst happen to x^y=y^x around e does. Though its also quite beautiful so id love an explanation
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*Runs away from thread in terror* 
Original post by FireGarden
Not as simple as you think. If exists then . This is obviously not true for all paths to in .
Take x^x=exp(xlnx). It suffices to show lim as x approaches 0 of xlnx is 0 which is easily done using l'hopitals by noting that x=1/(1/x)
Original post by newblood
Take x^x=exp(xlnx). It suffices to show lim as x approaches 0 of xlnx is 0 which is easily done using l'hopitals by noting that x=1/(1/x)
This limit is not good enough. You can of course have a number to the power of a different number, and to take that into account, you need to approach from any possibility; therefore we must consider . Now I agree, , but that is only one case of the required limit (along the line y=x towards the origin).
Consider the limits ; and . These limits are clearly not equal, hence there is no unique, sensible value for .
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