Thursday, 28 November 2013

real analysis - How to define the 00?











According to Wolfram Alpha:




00 is indeterminate.





According to google:
00=1



According to my calculator: 00 is undefined



Is there consensus regarding 00? And what makes 00 so problematic?


Answer



This question will probably be closed as a duplicate, but here is the way I used to explain it to my students:



Since x0=1 for all non-zero x, we would like to define 00 to be 1. but ...




since 0x=0 for all positive x, we would like to define 00 to be 0.



The end result is that we can't have all the "rules" of indices playing nicely with each other if we decide to chose one of the above options, it might be better if we decided that 00 should just be left as "undefined".


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