And this is why you should prove a solution exists before you calculate it :-)
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Well, not necessarily before, if you’re in a hurry, but definitely after... :)
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Most have figured out, as taught in grade school, that you have to go back to the original equation and make sure your solution works. Writing a= √2, what is the limit of a, a^a, a^a^a, ...? i: prove sequence is increasing ii: bound it by changing top a to 2 (What is a^a^2?..)
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a ^(b^(c)) = a ^ (b.c) and not a ^ ( b ^ c). So 3 ^(3 ^(3)) = 3 ^ 9 not 3 ^ 27.
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yeah but a^b^c = ((a)^b))^c not a^(b^(c))
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Who wrote this? The proof in the green box is definitely not by induction
https://en.wikipedia.org/wiki/Mathematical_induction?wprov=sfla1 … - Još 1 odgovor
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The series diverges for x > 1
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It actually converges for all x between e^-e and e^(1/e). I dont have a proof, so if you find one, let me know
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This proof is faulty, because √2 doesn't actually exist.
#askpythagoras - Još 2 druga odgovora
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