Re: infinity

sci.math_20050119_b:
So a problem with, or reason to abandon the notion that, the numbers
can be defined in that way is that it implies the infinite set of
finite integers contains an infinite element, which while conceptually
feasible in terms of ubiquitous naturals and the set of all sets
containing itself, is still not a clear issue.

sci.math_20050119_b:
Where there is some least positive (infinitesimal transcendental) real
called iota, and integral multiples of iota are representative of the
real numbers and necessarily not translatable to "definite" real
numbers, except in terms of scalar infinities (x/2x = 1/2), then the
set of reals is a contiguous point set on the real number line, besides
being a field.

sci.math_20050119_d:
Then, in consideration of the reals and a well-ordering of the reals,
besides facile rationalizations of the normal, linear, total ordering
as a candidate for a well-ordering, another line or direction of
enquiry is which properties a well-ordering specifically of the real
numbers would have to have besides just the characteristics of a
generic well-ordering because of the properties of the real numbers as
being comprising each point on the line and being at once an infinite
field with multiplicative identity.

.

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