The axiom of mathematics


The set of natural numbers is infinite









The order of the universe is the order of the natural numbers. In this order some few digits  conventionally chosen as digits: 0,1,2,3,… in this usual order   are combined to an infinite sequence of finite digit sequences.  From the order, in which the single digits are formed to a finite sequence, we immediately recognize, where this sequence is situated within the sequence of all such sequences.

We know about the serial law of the natural numbers. We do not know about this law yet, what concerns the writing of  living  nature. We can read this writing as (sequence of) natural number(s). The discovery of the DNS- Structure showed that the whole - living - nature is nothing than a calculation at all. Nature played with four letters C, G, D, T to establish all of its own. We do not know however, what the order, in which the four different DNS-Bases C, T, G, D are  seemingly completely irregularly  in each case set, has to mean. We deciphered this language in the meantime; we cannot read it yet. We do not know about the serial law of such a sequence of bases. We are missing syntax and semantics of this writing.

The natural numbers form in a far larger extent than one had so far noticed the basis of the whole of mathematics. The real numbers are the limit set of the procedure for the representation and production of the set of natural numbers, as the thesis of this web-presence:  "  The limited infinity of the natural numbers" shows. The real numbers for their part figure in mathematics and physics as image of the continuum sizes space and time. It is this  one and unique  serial law of the set of natural numbers, which establishes  also these continuum sizes. That is all we need for that. The whole universe reduces thus on this serial law  the only working world formula  faithfully the moth of Leibniz` "Dum Deus calculat, mundus fit". The key to the deciphering of the language of nature lies hidden here.

Life Sciences will advance  just as the experimental sciences  exactly to the extent in which they succeed in making mathematics obliged to its purposes. That is like a law of nature.

The language of mathematics is the language nature is written in, too. The vocabulary of this language is delivered from the natural numbers and its systematically extensions to other sets of numbers as the entire, the rational and irrational numbers. Therefore all of our attention has to be focused on the production of these numbers that is the procedure, which produces all of the sequences these numbers. For this reason the following text devotes itself to an analysis of the phenomenon sequence. That is the medium in which every language is written. A transfer of information can only be performed this way.

An analysis of this phenomenon is therefore as elementary as it is fundamental and central. In this medium numbers  and with them the whole of mathematics  find its representation and justification. For this purpose, however, we have to begin with far more originally as this generally happens in mathematics and philosophy. We have to do so and we can do so. The set-theoretical reasoning used in this disciplines does not come up to the reality of these numbers. Sequence says more than mere number. We can have it say more and in the system of the production of the sequence of finite sequences representing the set of natural numbers this phenomenon indeed says more. In each of these sequences the entire system of all of these sequences is present. From every such sequence we are told  and we can be told only from actually regarded sequence  where we are with this special one sequence within the totality of these sequences. We have not to count any more for this purpose, these sequences  and only these sequences  counting itself for their own.

In the models of mathematics and philosophy there is no possibility to count. These models are not autonomous, and they are not communicative. The reality they presuppose as something given is not equalized by their description. There is by assumption more at the beginning as is presented by construction at the end. It is much better to concentrate oneself from the beginning on this reality for itself. There is no question about the representation of the natural numbers any longer then,  being  positioning ourselves in the centre of the production of these numbers at there own.