At exactly the same time a direct method is necessary for the fresh new evidence of the latest compatibility of your own arithmetical concepts
It is extremely a network off things whose shared relations is actually influenced from the principles install and also for and that all of the http://datingranking.net/pl/soulsingles-recenzja/ offres, and only those individuals, was genuine which is derived from the brand new basics by an excellent finite quantity of analytical techniques
However, first and foremost I would like to specify the second while the vital one of the many concerns that is requested that have mention of the brand new concepts: To show that they are not inconsistent, that’s, one to one particular number of analytical procedures centered him or her is also never end up in contradictory results.
Within the geometry, the newest proof of the new being compatible of the rules should be affected by the building the ideal field of number, in a fashion that analogous affairs between the numbers of that it community coincide towards the geometrical principles. One contradiction regarding deductions regarding geometrical principles must with this become recognizable in the arithmetic with the realm of number. Similar to this the required research towards the compatibility of the geometrical concepts is designed to rely upon the brand new theorem of one’s being compatible of one’s arithmetical principles.
The newest axioms away from arithmetic is basically nothing else as compared to identified statutes from formula, by the addition of the brand new axiom from continuity. I simply accumulated her or him and in therefore starting changed the axiom from continuity because of the several smoother maxims, namely, the better-understood axiom regarding Archimedes, and a different sort of axiom essentially the following: you to number form a network from things that is capable of not any longer extension, so long as all the rules hold (axiom away from completeness). (more…)