Purpose of a monotonic transformations in utility functions Based on my economics book, monotonic transformations for a utility function can look something like this:

$f(u) = u + 17 $ or even like this: $f(u) = u^3$

That being said what it purpose in the case of the utility function, as far as I know, the number of the utility doesn't matter to us (the only thing that matters is if it's bigger or smaller than the utility of another bundle)?

The book explains it in the following way:


  monotonic transformation is a way of transforming one set of numbers into
  another set of numbers in a way that preserves the order of the
  numbers.


Though it the order stays the same why would we do it in the first place?
Certain calculations using utility require utility functions to have some particular properties. The point of bringing up the invariance of preferences represented by different utility functions that are just monotonic transformations of each other is to show that these utility-based calculations are not entirely dependent on the utility functions that you happen to choose. The same results should at least hold up to order-preserving transformations.