File:X-lbx.pdf
Summary
| Description |
English: Plot of the function f(x) = x - lb(x). It is defined for all real numbers x>0, its derivatives are f'(x) = 1 - 1/x·ln(2) and f''(x) = 1/x2·ln(2). Hence, it has a local minimum at x=1/ln(2), and no inflection points; it is strictly decreasing and increasing left and right of its minimum point, respectively. The restriction of f to each of these domains is injective, and thus has an inverse. The function is repeatedly used in proofs about Kolmogorov complexity. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:X-lbx.pdf - File:X-lbx svg.svg |
Gnuplot source code |
|---|
# 2^x = y = e^(ln(2)*x)
# lb(y) = x = ln(y)/ln(2)
set xrange [0.0002:16]
set yrange [0:12]
set xtics 1
set ytics 1
plot x-log(x)/log(2) with lines lw 2 lc 7 title ""
pause -1
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