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@LouisIngenthron Also it bears mentioning that as much as you may believe 1+1=2 is a universally and objectivelly true fact it is not. It is only true under an explicit definition of that being so, and depends on every definition therewithin.

For example 1+1 does nto equal two in the following systems:

in base 2 systems there is no symbol such as 2 so "1+1=2" is patently false. however "1+1=10" is true under that system. This is because our definition of the numbers and how they expressed is different.

In braurer groups addition is defined as a tensor product over algebras. Without getting too technical under this mathematical ring "1+1 does not equal 2" in fact this very assertion is non nonsensical.

In noncommunicative addition rings then "1+2 is not equal to 2+1" and in many such rings 1+1 equals something other than 2 as a consequence (in some such rings it does).

Similarly in mathemetical rings the very set of numbers that exist may be finite, and the number 2 may not exist at all. In fact you can have mathematical rings where 0 and 1 are your only numbers, and as such "1+1=2" is not true.