the purpose of this post is an attempt tp show that real numbers set could be generated intensively,it also could be counted somehow by defining aspecial surjective or injectice function.i think the mathematical constructure of this post need to be fixed by an expert,thats why i need some help here.(adsbygoogle = window.adsbygoogle || []).push({});

Consider we express the tow positive real numbers ,A&B as,

A=Σam[(10)^(n-m)] B=Σbm[(10)^(n-m)] Where,( n,m=0,1.2,……) am,bm,positive integer Now if, am+bm=pm+10,pm<10 pm,positive integer Then we define the relationship R, ARB={pm*(10)^(n)}+{(pm+1)*(10)^(n-1)+..... Obviously, R; looks like adding backwards.e.g, 341R283=525 =(3+2)=5,(4+8)=12,(1+1+3)=5 Lets now pick up arbitrarily the infinite sequence

S0=Σn\(10)^(n),+Σn\(10)^(n+1) + Σn\(10)^(n+2)+.....

Where n=1to9 ,10to99,100to999 ,...etc.respectively

i.e, S0=0.123456789101112131415161718192021222324.... ,. In order to generate or count* the real numbers within the interval,e.g. (0,1),

We define the surjective function,F;

F:N→positive irrational numbers subset in(0,1)

Where ,

F(n)=SnR0.1,

Sn, the set of sequences,

S1=s0 R 0.1,

S2=s1 R 0.1,

Sn=Sn-1R0.1,

etc.

notice that (n-1) is suffix,

post(1)

There are an infinite sequences,s1,s2 that we can make S1RS2 Close enough to any real number.

post(2)

if the relation,R,has aseriouse mathematical use , can we solve equations of the form,

xRx=s,where,s=0.3,0.5,..etc ,or xR1=10? i mean can the relation,R,be generalized to involve such equations?or even negative numbers?

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# Real number set and countablity

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