[jlgreco]

You absolutely need those things for a great deal of modern programming. All modern programming? No, but a great deal.

Without that they would have been at a disadvantage. I don't see what is so hard about this concept to you.

Regardless, the simple historic fact remains that Babbage and Ada were both unable to build the machine, and unable to verify their suspicion that the machine was special, and unable to effectively communicate to their peers this suspicion. The prerequisite math for all three of these tasks did not yet exist.