The notation "log n" represents the logarithmic function, which is the inverse of the exponential function. In this context, it is used to measure the growth rate of a function in terms of the input size n.
For large values of n, the function "log n" grows much slower than the function "O(n^ε)". This means that the value of "log n" will be much smaller than the value of "O(n^ε)" for the same input size n.
This inequality indicates that the function "log n" is an upper bound on the function "O(n^ε)" for large values of n. In other words, the growth rate of "log n" is always smaller than the growth rate of "O(n^ε)" for large input sizes.
One example of a function that satisfies this inequality is "log n" itself. For any value of ε greater than 1, the function "log n" will have a smaller growth rate than the function "O(n^ε)" for large input sizes n.
The growth rate of "log n" is considered to be slower than linear growth (O(n)), but faster than constant growth (O(1)). It is also slower than polynomial growth (O(n^c)) for any constant c, but faster than exponential growth (O(2^n)).