The big O specifies 2 positive constants c and n_0 but there can be multiple c and n_0 values that are solutions. How can we decide which one is the best. What does having multiples solutions signify ?
In: 5
It characterises the growth rate of a function; completely different functions can have very similar growth rate (especially toward the limit).
What domain are you learning this in? As in some disciplines/uses the values of x could be restricted to positive integers, rather than positive real numbers or complex numbers with a positive real part.
Constants can be ignored especially for those f(x) which are multiplicative eg f(x) = 5x^3 + 17x^2 + 3x. As x gets large, the x^3 term dominates more and more and the constants, 5, 17, 3 more and more irrelevant. So you could set that 17 to 1 and it will not make a big difference to the big-O evaluation of the function: it’s polynomial.
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