🎓 Dr. Freemo :jpf: 🇳🇱 on Nostr: npub1ktvle…4fv3a Also it bears mentioning that as much as you may believe 1+1=2 is ...
npub1ktvleg4d765hrvqh7sx3fm6z5lxwgl8ef58fvt530nlcz2jea4hqg4fv3a (npub1ktv…fv3a) 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.
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.