Cache: http://webcache.googleusercontent.com/search?q=cache%3Ahttp%3A%2F%2Fwww.xamuel.com%2Fusing-wolfram-alpha-to-prove-10%2F http://webcache.googleusercontent

Cache: http://webcache.googleusercontent.com/search?q=cache%3Ahttp%3A%2F%2Fwww.xamuel.com%2Fusing-wolfram-alpha-to-prove-10%2F http://webcache.googleusercontent.com/search?q=cache%3Ahttp%... Unfortunately the author seems uninformed. He claims that 0^0 = 1, not indeterminate which is what Wolfram Alpha claims (and as anyone knows, if you use indeterminates you can prove any number equals any other number, which the author does in uncached screenshots). The problem though is that 0^0 changes its meaning depending on the context. If you have an function f(x,y) = x^y, it's not continuous at (0,0) because the limit of x -> 0 is 0 and the limit y -> 0 is 1, making the value undefined! (Which is still different from 1, 0, or indeterminate.) I used to know of a better blog post on the issue, but here's http://mathforum.org/dr.math/faq/faq.0.to.0.power.html http://mathforum.org/dr.math/faq/faq.0.to.0.power.html Oh wait, I found it: http://www.askamathematician.com/?p=4524 http://www.askamathematician.com/?p=4524 "Zero raised to the zero power is one. Why? Because mathematicians said so." Sort of in the same character of dispute is the fact that 0 and 1 aren't probabilities: http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/ http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/ I'm also unsure what the author is entering since the screenshot isn't cached. If I try http://www.wolframalpha.com/input/?i=summation+x^n%2Fn!+from+n%3D0+to+infinity+where+x+%3D+0 http://www.wolframalpha.com/input/?i=summation+x^n%2Fn!+from... wolfram gives the correct e^0 = 1. Edit: Ah, he's using http://www.wolframalpha.com/input/?i=summation+0^n%2Fn!+from+n%3D0+to+infinity http://www.wolframalpha.com/input/?i=summation+0^n%2Fn!+from... (substituting 0 in explicitly instead of instructing Wolfram to substitute on x) which is quite an interesting quirk to give 0.