spiral of irrationals

[AntonioLao]

The set of irrationals not including por any of the irrational fractions can be generated by using Pythagorean Theorem starting with 1²+1²=a². Here a is the irrational square root of 2. Then 1²+ a² = b where b is square root of 3. 1²+b=c where c is square root of 4. 1²+c=d where d is square root of 5. 1²+d=e where e is square root of 6. 1²+e=f where f is the square root of 7. 1²+f=g where g is the square root of 8. 1²+g=h where h is the square root of 9. 1²+h=i where i is the square root of 10. 1²+i=j where j is the square root of 11. 1²+j=k where k is the square root of 12. 1²+k=l where l is the square root of 13. 1²+l=m where m is the square root of 14. 1²+m=n where n is the square root of 15. 1²+n=o where o is the square root of 16. 1²+o=p where p is the square root of 17. 1²+p=q where q is the square root of 18. 1²+q=r where r is the square root of 19. 1²+r=s where s is the square root of 20. 1²+s=t where t is the square root of 21. 1²+t=u where u is the square root of 22. 1²+u=v where v is the square root of 23. 1²+v=w where w is the square root of 24. 1²+w=x where x is the square root of 25. 1²+x=y where y is the square root of 26. 1²+y=z where z is the square root of 27.

These demonstrated that the square root of positive integer between 2 and 27 only contain 4 perfect squares: 4, 9, 16, and 25 implying that the cardinality of irrationals is greater than that of the rationals. The universe is more irrational than it is rational, more incomprehensible than comprehensible. When these irrationals are mapped into the unit circle then it will include the irrational number p, which are already thoroughly analyzed in complex analysis.

[mkirkpatrick]

Does this mean then Antonio that we can use an irrational spiral to gain access to a mobius strip,thereby accessing consciousness in its purest form?


regards michael.

[AntonioLao]

we can use an irrational spiral to gain access to a mobius strip

But my problem is how to sidetrack zero cardinality and zero ordinality of the Moebius strip?

[mkirkpatrick]

But my problem is how to sidetrack zero cardinality and zero ordinality of the Moebius strip?

Somehow we need to "head them of at the pass"!



regards michael.

[AntonioLao]

head them of at the pass

Now that I thought about it some more the cardinality of the Moebius strip is really infinity. How we head off infinity seems impossible to me.

[mkirkpatrick]

Now that I thought about it some more the cardinality of the Moebius strip is really infinity. How we head off infinity seems impossible to me.

Maybe they are one of the same thing?So we are already in,soto speak?



regards michael.

[AntonioLao]

they are one of the same thing

This is true for 2 arbitrary circles: one of unit radius and the other of infinity radius. By one to one correspondence, a mapping maps completely every point to the other, vice versa.

[mkirkpatrick]

This is true for 2 arbitrary circles: one of unit radius and the other of infinity radius. By one to one correspondence, a mapping maps completely every point to the other, vice versa.

There is a universal law of corrospondence which would be able to relate this into a
whole,which would solve the difficulty.



regards michael.

[neutralino]

Now that I thought about it some more the cardinality of the Moebius strip is really infinity.

Cardinality is normally, at least colloquially, described as a measure of the number of elements in a given set. I'm not quite sure what you mean by the cardinality of a surface: are you talking about the number of points on the surface? Also, a cardinality of infinity doesn't really mean much: as you mention above, the number of elements in |R is greater than the number of elements in |N, but they are both infinite sets. What do you mean by a cardinality of infinity here?

[AntonioLao]

are you talking about the number of points on the surface

Yes. In a previous thread, I stated that the cardinality of an arbitrary circle is greater than the cardinality of an infinitely extended straight line even though both contain infinite number of points. It can be demonstrated by functional 1 to 1 correspondence transformation. if this is true for curves then it is also true for surfaces as they are mapping from R to R*R.