A Semi Number-Theoretic approach and Proposed proof that CH is false.
Résumé
We introduce number theoretic systems for use into the study of subsets associated with the reals. We will then show that such sets possess different cardinalities, whilst having cardinality greater than that of the naturals. In mathematics, especially with new mathematics, there is a huge difficulty in drawing an entire picture of its usefulness in solving a particular problem or its effectiveness in the way of a theory in just a few lines, yet this is necessary, as very few will want to undertake the understanding of a new concept if one does not see its potential immediately! So in the next few lines, we will aim to draw a picture of the usefulness of number theory in the resolution of CH. The time is ripe for many such pictures as was expressed in a Lecture by Matt Foreman, University of California, Irvine. Therein was described all mainstream set-theoretic attempts at resolving CH with concluding remarks surrounding other possible un-ventured possibilities which the writer writes "There are viable alternatives to the Woodin 'Solution' of the CH and these should be considered and explored before we rush to celebrate." Many such attempts pioneered by W.H.Woodin involve a logical concept of models, as our approach is far from set theoretic we will not explore this concept beyond this mention. Mathematic should not be just about finding an answer but more about understanding it. More specifically instead of some reducto et absurdum resolution to CH, a more appealing anwser would express in conjunction with such an argument, (much like the original diagonalization) what specific property possessed by numbers disallows/allows a grouping of numbers so as to form a cardinality N1/N0 ˂ lt; N1 ˂ 2^N0 .
Domaines
Mathématiques générales [math.GM]
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