Now you're cheating, because + and - no longer mean "addition" and "subtraction", but merging and... well, weird division - the last example would be better as 1 stick / 2 = 2 sticks.
But try the first two with the following substitutions:
You added additional axioms that require a quantity. Not all things exist as quantities with properties of addition, multiplication, division, or subtraction. Various debates can be had that any quantity is largely an arbitrarily defined border.
The point mostly being, any symbolic representation is only that. It is never universal. And to think it’s an objective representation of anything is serious error.
Sure we can measure something else to keep a track of whats happening and fit our definitions, but the math remain true, isn't it? It is still 1 river and 1 drop and 2 sticks.
You are correct when you say its not a defined measurement. And that is the point. Not defined in math.
Math is our reality, and not a universal reality/law/principal (while science conservation of energy/matter is universal). There are no addition/subtraction happening in the universe.
Addition is not conservation. But that's how we see it.
It’s one of something. When one of something and one of another thing are observed it’s expressed as 1 and 1 so two rivers become one they represent a quantity of observation.
Then as 1 and 1 totaling two rivers they come together then exist as 1.
Representation is relative on an arbitrary border of quantity. The rules leak for any rule that exists.
One father and one mother have a kid. One and one make another one totaling three.
• and • make •.
Usually a person will substitute 1 for the observation of a “thing” so • will be father, and another • mother +1+1=+1
One unit and another one unit makes a third unit. Yet one unit plus another unit is two units.
> It’s one of something. When one of something and one of another thing are observed it’s expressed as 1 and 1 so two rivers become one they represent a quantity of observation.
Not really. If I look at a map and see the Amazon river, and then see the Nile, Amazon + Nile ≠ 1 river. They're still two separate rivers. Adding rivers means merging sets of rivers under consideration, not merging actual rivers.
All you're doing now is playing with different operations that are not what the symbol "+" stands for.
I don’t think that you’d be able to communicate the observation of units in a way that’s consistent as a written form of symbology in the rule space of mathematics and the language space used to communicate the mathematics and observation of reality around oneself which leads to relativity.
All definitions are nuanced and subjective based on path of least resistance heuristics.
It’s often miscommunication is happening because expected results are misaligned despite using same rules/language.
It’s quite complex. It’s really interesting but also leads to poor communication. Do we try to embed in our cultures to align on expectation and values to improve this or always doomed to potentially fatal inconsistencies? I guess the dynamics of any rules naturally incentivize behavior whether it’s negative or positive.
1 does not equal "1 of <something>", the latter is a concrete example only (and as mentioned the quantity error, you would have 2 drops of water if the volume of 1 drop stays consistent).
1 is an abstract concept applied to many things that share this "singleton property".
I disagree, computation has equality, unless you think computer files are not real. Two computations can be equal, and as far as we know we are leveraging this property of the universe. Electrons move and produce patterns which have equality and gives rise to computer state and thus equality of values, not to mention electrons themselves must be indistinguishable given they behave the same.
1 river + 1 river = 1 river
1 stick - 1/2 stick = 2 stick