The discussion revolves around the interpretation of the notation for logarithmic functions, specifically the meaning of ##\log^3 n## versus ##\log^{(3)} n##. Participants explore the implications of these notations in mathematical contexts, including their potential for confusion regarding repeated multiplication versus function composition.
Participants express differing views on the interpretation of logarithmic notation, with no consensus reached on the correct meaning of ##\log^3 n## versus ##\log^{(3)} n##.
The discussion highlights the ambiguity in mathematical notation and the importance of context in interpretation. Participants note that different conventions may apply in various mathematical fields.
That's the one you want.22990atinesh said:or ##\log^3 n = (\log n)^3 ##
HallsofIvy said:It is not uncommon to put a an exponent in parentheses to indicate a repeated composition.
That is, [itex](log(x))^{(3)}[/itex] or [itex]log^{(3)}(x)[/itex] is "log(log(log(x)))".
Unfortunately, that is also often used to indicate the third derivative so you must be careful to state which!
Mark44 said:In exactly the same way, cos2(x) does not mean cos(cos(x)), but rather it means cos(x) * cos(x) = (cos(x))2. The exponent indicates repeated multiplication, not repeated function composition.
The above is what HallsOfIvy said. I haven't seen it, myself, but I have seen f(3), with parentheses around the exponent, to indicate the third derivative.22990atinesh said:You mean ##\log^{(3)} n = (\log n)^{(3)} = \log (\log(\log n))##
This is what I said.22990atinesh said:##\log^3 n = (\log n)^3##
I know, I was just rechecking from you. :)Mark44 said:The above is what HallsOfIvy said. I haven't seen it, myself, but I have seen f(3), with parentheses around the exponent, to indicate the third derivative.
This is what I said.