One of the principle objects of abstraction is economy of effort. Any 4 year old will quickly learn that adding 3 apples to 2 apples will yield a comparable result to adding 3 cars to 2 cars. Once she has conceptualised the idea that “2+3=5” regardless of what is being added, her answer when asked what 2 trees added to 3 trees is will be forthcoming much quicker than before this realisation. No longer will she have to go out and find a forest in order to determine the result. Likewise, when elementary algebra is first introduced in high school, a great saving of time is achieved when a student is able to say that x + x = 2x for an infinite variety of x values, without having to confirm this for each individual case.
Definitional challenge 