The number of internal nodes of a binary tree cannot exceed the number of leaf nodes. Proving this will require the use of symbols. To define a complete binary tree, for instance, I will need to make use of the compound symbols, complete, binary, and tree. Another one, geometric, jumps in and dares me to do without it.
Proving the convergence of a series is a task that only a philosopher would set for himself. Once done he (or she) is likely to meet with a world of examples which demonstrate that the fact was obvious all along.
The Ancients are often referred to, but some of the stories don't hold water. It does seem to be the case that they knew that to give a symbol for 1/0 was as sensible an idea as to make a smiley face part of the alphabet. There are exactly two places that the symbol may be used in place of a number; and both of them lead us to the contemplation of the Cartesian Plane.
The Cartesian Plane existed before it was named, but once it was understood when infinity and its inverse may be used, we no longer needed to refer to the ancients and their political struggles.
Those who don't like mathematics very often yet like to use the conclusions that are reached. It would be beyond ridiculous not to use the stated fact when allocating memory for a binary tree. Sure, it's obvious; but so is it obvious that the teaching of geometry was only setting us up for a fall.
Now that I will probably be asked to prove. But I don't know if I'd be willing to do so without showing my face.