Defining Number : Differring from Peano and Tibees

Watch video:

A delightful proof that 2+2=4
Tibees | 26.IV.2019
https://www.youtube.com/watch?v=0-pL2J0ZB8g

Now read my comment:

I disagree with 0 being a natural number.

Both number and geometry start with 1 single whole - a thing that any existing thing can be described as.

The numbers go by parallel entities, by adding 1 to 1, geometry goes by dividing the whole into parts.

So, here is how I would go about proving 2+2=4.

Transitivity and the rest are granted, it's where you start the five propositions that I disagree with first one.

2 = 1+1 (by definition)
+2 = +1+1 (by transitivity from first)
3 = 2+1 (by definition)
4 = 3+1 (by definition).

Proof with this in mind:

2+2 = 2+1+1
2+1+1 = 3+1
3+1 = 4

2+2 = 2+1+1 = 3+1 = 4
(by transitivity) = > 2+2=4

0 and -1 are perfectly valid "relative numbers" as they are called in France, or "numeric relations" as I would prefer to call them, precisely as "twice" or "half" are geometric relations.

+-0 is in arithmetic what *1/1 is in geometry.