# Mathematical Proof

## Mathematical Proof

Sequence of logically ordered statements based on a certain number of hypotheses and that should lead to an expected conclusion.

The proof can involve results that were previously demonstrated or other statements of the theory such as axioms, postulates or definitions of terms in the theory.

The term “proof” is synonymous with “demonstration”.

### Example

Here is an example of casting out nines:

Algorithm to verify the accuracy of an arithmetic operation on whole numbers in which we apply the same operation to the sum of the numerical values of the digits of the numbers involved (digital root or DR), after these numbers have been expressed in modulo 9 form.

Operation:  467 + 679 =  1146

The digital root of 467 is 17, because: 4 + 6 + 7 = 17
The digital root of 679 is 22, because: 6 + 7 + 9 = 22
The digital root of 1146 is 22, because: 1 + 1 + 4 + 6 = 12

 467 + 679 = 1146 RN 17 22 12 RN 8 12 4 3 RN 3 = 3

Therefore: 12 is congruent with 3 modulo 9 and the sum 1146 of 467 and 679 is correct.