Re: infinity

sci.math_31027:
Well, there are infinitely many orders of finite-ordered polynomials.

sci.math_31027:
Then there are infinitely many coefficients.

sci.math_31027:
Do you say the algebraics are countable? There exists a one-to-one
function from them to the Cartesian product N and itself infinitely
many times. The Cartesian product of N and itself infinitely many
times is uncountable, just ask Ullrich or Virgil.

sci.math_31027:
The polynomial has finite rank, or order, degree, and its rank can
range from zero to infinity. That's very similar to an integer, an
integer is finite, but there are infinitely many of them. The
polynomials rank is an integer.

sci.math_FE_Equation:
The derivation considers all of the infinite sequences of binary
values, zero and one, 0 and 1. The first thing to notice is among all
of the sequences A, at a given index i in the sequence half of the
sequences have a value of zero and the other half have a value of 1.

sci.math_FE_Equation:
Here it is convenient to consider the infinite bit sequences as being
representative of the expansions of the reals between zero and one
inclusive, yet the same should hold true for all reals.

sci.math_FE_Equation:
In the case of the infinite bit sequences, n->oo.

sci.math_FE_Equation:
Here's the major assumption: half of the sequences of A contain equal
numbers of zeros and ones. Thus the probability of an infinite
sequence having equal numbers of zeros and ones is 1/2, that is to say,
P = 1/2.

sci.math_interview:
There aren't any paradoxes, the existence of one woud be paradoxical.
That's one of those statements I try to use to examine background
mathematical logic in terms of plain statements, like "if there are
infinite integers there are infinite integers" and "the order type of
all ordinals is less than nothing", or even "if for every set X there
exists x in X then X is not empty."

sci.math_interview:
I'm probably jealous. By the same token, some of his concepts I don't
find apparent. I do have some problems with people saying that sets'
sizes aren't comparable besides via cardinality. For example, half the
integers are even integers, x/2x = 1/2 for all x, and infinitesimal
analysis proffers geometrically provable and empirically true results.
There are results of uncountable sets being countable unions of
countably many sets.

sci.math_interview:
I wish I knew it better. I do appreciate that in some form it is an
infinitesimal analysis, with the integral bar being an S for summation
and dx standing for scalar infinitesimal x. That leads into one thing
I think deserves more examination: scalar infinity, where when y is a
dependent variable of x that x=y as x goes to infinity, and that 2x/x
always equals 2, even at some infinite value, a scalar infinity. That
has there being one scalar infinity of scalar infinitesimals in the
unit interval.

sci.philosophy.meta_20050610:
Basically my reaction is that there are extremes and their mediation.
For something like the numbers, the integers, basically
sequentialization from induction leads to these distinct ordinals.
Their very difference leads to more or less a constant difference
between them, but also at the level of an "infinite perspective" there
are ways to consider their difference as variational. In reusing that
conception of a circularized infinite sequence, as the origin is
everywhere, mathematical facts are basically the most obvious true
things after tautology.

.

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