Bluedoom Posted May 7, 2013 Share Posted May 7, 2013 Dunno if this should be in General, SD or Ftff but I'll leave it here for now.Today my friend was trying to derive x^0=1 and he did it by:Take y= x^0He takes log on both sides and the result is confirmed except logs are nothing but the representation of exponents, so you can't prove it by using logs.So the conclusion is that a^0 is nothing more than an axiom. Hmmmm...http://www.math.toronto.edu/mathnet/questionCorner/powerof0.htmlReason 2 sounds interesting. It goes into the philosophy realm of having an object in the first place, meaning that reason would work only if we had the definition of an object.Reason 4's also pretty interesting. Never thought of that.Never thought of Reason 1 either but I always thought defining an exponent would work only once one defines it for the power 0 and for the power 1.Oh and also, I just thought of a statement."A paradox can be made out of anything." Seems very similar to the Socratic paradox.Yeah I think I just feel like thinking about small stuff now. XD Quote Link to comment Share on other sites More sharing options...
eclipse Posted May 7, 2013 Share Posted May 7, 2013 Serious Discussion - NO. This really isn't up for debate. General - Eh. FftF - Depends on the responses you get to this thread. Quote Link to comment Share on other sites More sharing options...
Green Poet Posted May 7, 2013 Share Posted May 7, 2013 If I remember correctly, the derivative of x^0 is factually 0 though? Reason 2 is out of the grasp of my comprehension, unfortunately, but I can see where the others are going. Interesting. . . Quote Link to comment Share on other sites More sharing options...
Bluedoom Posted May 7, 2013 Author Share Posted May 7, 2013 Err sorry by derive I didn't mean the derivative I just meant how we obtain that result. Quote Link to comment Share on other sites More sharing options...
Grace Posted May 7, 2013 Share Posted May 7, 2013 (edited) (a^n)/(a^n) = a^(n-n) = a^0 but dividing two identical numbers gives 1 by definition so therefore a^0 = 1 there I fixed it for you. edit: not sure if that's quite what you want but it's as good an answer as i got. Edited May 7, 2013 by Manix Quote Link to comment Share on other sites More sharing options...
Bluedoom Posted May 7, 2013 Author Share Posted May 7, 2013 (edited) yeah, figures I made this complicated for myself. >_> EDIT: Well on second thought I was thinking of getting that result without using exponents i.e how would you define x^0 as a base for all exponent forms and such but that still works. Edited May 7, 2013 by Bluedoom Quote Link to comment Share on other sites More sharing options...
Green Poet Posted May 7, 2013 Share Posted May 7, 2013 Err sorry by derive I didn't mean the derivative I just meant how we obtain that result. Ooh, my bad. Gonna look over these again with that in mind, haha. Quote Link to comment Share on other sites More sharing options...
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