In my opinion we can consider both chances as being true. Mathematicians are constantly inventing new mathematics when they set up the rules for their functionality. Then, after those “games rules”, they find new consequences of those rules, which are called theorems, corollaries, axioms and postulates.

So as to clarify the answer that was previously asked: `1 + 1 = 2` Is this a discovery or an invention? Common-sense makes us to believe that it is a discovery since it is a universal truth and has always been like that for a long time till now. However, all of us are able to recognize that the symbolism used in this operation was invented and any means that result is not always true, because it depends on the Maths that is used. Let's see the following:

- `1 + 1 = 10` according to binary math;
- `1 + 1 = 1` according to boolean math;
- `1 + 1 = 0` according to modular math (mod 2).

Having all this in mind, I think it is obvious that the rules had to be invented and then the findings appeared.

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