Re:The Oxford maths interview, shaking up admissions
by jamessb on Friday March 04, 2016 @07:45PM
(#11227839)
How so?
The important parts to include on a sketch are that the function is monotonically increasing, has an asymptote at x=1 [0], intercepts the x-axis at x=e (approx 2.7) and quickly becomes almost flat. Both graphs agree on these points.
Wolfram Alpha is using the complex logarithm (https://en.wikipedia.org/wiki/Complex_logarithm) to extend to x < 1; Google isn't. I'm fairly sure an interviewer would expect a sketch that looks like Google's, perhaps with a comment that achieving ln(ln(x)) < 1 is possible (only) if the ln function is allowed to take complex values.
[0]: For values of x < 1, ln(x) < 0, so ln(ln(x)) is not a real number.
The important parts to include on a sketch are that the function is monotonically increasing, has an asymptote at x=1 [0], intercepts the x-axis at x=e (approx 2.7) and quickly becomes almost flat. Both graphs agree on these points.
Wolfram Alpha is using the complex logarithm (https://en.wikipedia.org/wiki/Complex_logarithm) to extend to x < 1; Google isn't. I'm fairly sure an interviewer would expect a sketch that looks like Google's, perhaps with a comment that achieving ln(ln(x)) < 1 is possible (only) if the ln function is allowed to take complex values.
[0]: For values of x < 1, ln(x) < 0, so ln(ln(x)) is not a real number.