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 Jan16 awarded Yearling Dec20 awarded Caucus Sep24 awarded Autobiographer Sep10 comment Limit factoring You need + under radical ... OP edited problem. :) Mar23 revised Domain and range of a function. Fixed typo Mar23 revised Domain and range of a function. Adendum Mar23 answered Domain and range of a function. Mar23 comment Simplifying a radical with fraction and sum Ahh , then we can get the result. Mar22 comment How can I formulate the two guards puzzle to disallow references to the other guard? Ahhh , thanx , buttons sticking ... Mar22 revised How can I formulate the two guards puzzle to disallow references to the other guard? deleted 1 characters in body Mar22 revised How can I formulate the two guards puzzle to disallow references to the other guard? added 126 characters in body Mar22 answered How can I formulate the two guards puzzle to disallow references to the other guard? Mar21 comment Whats the name of this sort of matrix The 17 looks 'out of place' to me , I would expect 12 in that position. :) Mar20 answered Simplifying a radical with fraction and sum Mar19 comment How does the exponent of a function effect the result? IMHO the interpretation, the presentation AND the intermediate steps are important. $$\frac{ 2}{2 } = 2 - 1$$ $$x^{ \frac{ 2}{2}} = x^{2 - 1} = \frac{x^2} {x}$$ Zero has been removed from the domain so this 'path' gives a ddifferent answer than the two cases asked by the OP. Mar19 comment How does the exponent of a function effect the result? There is freedom to play $$-1 = (-1)^1 = (-1)^{ \frac{ 2}{2}} = ((-1)^{ \frac{ 1}{2}})^2 = (\pm i)^2 = -1$$ Mar19 comment How does the exponent of a function effect the result? There are 4 4th roots of 1, One of the roots is $i$ , the right answer. What would really be devastating is if we used 'seemingly legitimate' algebra to get 4 roots and $i$ was not among them! :) Also , there is no problem if n is odd. Mar12 comment Why are mathematical results discovered by multiple people independently? I'm fearful (like Columbus) that this thread may be closed by 'The Powwers That Be' and we lose our interesting discussion. My reference to Columbus is in the context of the usual historic interpretation that this magnificent explorer that braved sea monsters and falling off the edge of the world was fearful of only one thing , THAT HIS MEN WOULD WANT TO TURN BACK! :) Mar12 comment Why are mathematical results discovered by multiple people independently? @sabyasachi , Ahh... I don't see it that way , it amuses me as a student of history. We should also refrain from swearing. :wink: Mar12 comment Why are mathematical results discovered by multiple people independently? @sabyasachi , L'Hospital had at least 5 names! LOL www-history.mcs.st-and.ac.uk/Biographies/De_L'Hopital.html