Harish Ramkumar
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E-mail Forwards 4 All - Isang Litrong Liwanag (A Liter of Light)
Isang Litrong Liwanag (A Liter of Light), is a sustainable lighting project which aims to bring the eco-friendly Solar Bottle Bulb to disprivileged communities nationwide. Designed and developed by students from the Massachusetts Institute of Technology (MIT), the Solar Bottle Bulb is based on the principles of Appropriate Technologies – a concept that provides simple and easily replicable technologies that address basic needs in developing communities.
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Q: What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree?
Clever student:
I know!
= = = = .
Now we just plug in x=0, and we see that zero to the zero is one!
Cleverer student:
No, you’re wrong! You’re not allowed to divide by zero, which you did in the last step. This is how to do it:
= = = =
which is true since anything times 0 is 0. That means that
= .
Cleverest student :
That doesn’t work either, because if then
is
so your third step also involves dividing by zero which isn’t allowed! Instead, we can think about the function and see what happens as x>0 gets small. We have:
=
=
=
=
=
=
=
=
=
So, since = 1, that means that = 1.
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