To try to resolve this, a list was produced of axioms which can be taken as self-evident. This means they can be assumed as first principles upon which all other theories can be built. However, even these axioms have not been immune to questioning - and, if you need axioms upon which you build the axioms, doesn´t that also mean you need axioms to build the axioms of the axoms....(

*ad infinitum*)? Anyway, these are the seven Axioms of Arithmetic:

- For any numbers
*m*,*n*:*m*+*n*=*n*+*m* - For any numbers
*m*,*n*,*k*:*m*+*n*) +*k*=*m*+ (*n*+*k*) - For any numbers
*m*,*n*,*k*:*m*(*n*+*k*) =*mn*+*mk* - There is a number 0 which has the property that, for any number
*n*:*n*+ 0 =*n* - There is a number 1 which has the property that, for any number
*n*:*n*x 1 =*n* - For every number
*n*, there is another number*k*such that:*n*+*k*= 0 - For any numbers
*m*,*n*,*k*, if*k*≠ 0 and*kn*=*km*, then*m*=*n*

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