Pure Mathematics (Pure Arithmetic) is redefined.

[Epsilon=One]

...........Mathematics does not
.........................explain Nature;
......................................Nature explains
.................................................m athematics.
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This post is in memoriam: Alfred Tarski ( http://en.wikipedia.org/wiki/Alfred_Tarski) [1901-1983]

Pure Mathematics (http://www.liv.ac.uk/maths/PURE/wipm.html) (Pure Arithmetic)
is redefined by Pulsoid Theory.[/CENTER]

Pulsoid Theory (http://www.physicsmathforums.com/forumdisplay.php?f=63) brings about a Paradigm Shift! in fundamental mathematics by unraveling the mysteries of pure mathematics (http://www.liv.ac.uk/maths/PURE/wipm.html) that underlie all physical manifestations.

Within Unimetry (http://www.physicsmathforums.com/showthread.php?t=129), the mathematics of Pulsoid Theory (http://www.physicsmathforums.com/forumdisplay.php?f=63), number systems are not dependent upon a “base,” which conventionally is, most often 10; or, digitally, 2; nor, are numbers contrived in any manner.

Pulsoid Theory (http://www.physicsmathforums.com/showthread.php?t=128) determines, in a consistent, geometric manner the value of One, for any system, from Natural manifestations, by an application of the Elliptical Constant (http://www.physicsmathforums.com/showthread.php?t=107); whereby, all other values (numbers) are then set, as algebraic expressions of established structural parts, as generated by Triquametric motion (http://www.physicsmathforums.com/showthread.php?t=101), rather than as uniform, or otherwise, units of a particular “base” scale.

Numbers are multiples of the Elliptical Constant (http://www.physicsmathforums.com/showthread.php?t=107).

The Elliptical Constant (http://www.physicsmathforums.com/showthread.php?t=107) is a fundamental phenomenon of every ellipse.

Ellipses are a heuristic representation of the most fundamental Natural pulse.

Not only are numbers so generated; but, also, all geometry, all arithmetic manipulation, orthogonal dimensions, time, acceleration, and the Inverse Square Law (http://www.physicsmathforums.com/showthread.php?t=120) are likewise generated.

Number values are not dependent on a scale of 10, or any other scale, as all values are directly, derived from the structure and relationship of values created by a certain class of ellipses that includes all elliptical shapes, which structures and relationships can be universally, geometrically expressed as values in any numbering system.

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[ste]

How are numbers represented in this new system? Can numbers be converted from base n to be represented as a multiple as "One"? Is there an algebraic function which allows us to use these new numbers? How are numbers related to one another using SIS (salient intrinsic structures)? What other interesting properties are found with these numbers? In what ways are they useful? In what ways can this number system have advantages over already existing (base n) systems?

[Epsilon=One]

How are numbers represented in this new system? Can numbers be converted from base n to be represented as a multiple as "One"?Yes, all bases are contrived except for base 2. Integers are represented as multiples of the Elliptical Constant (www.CQthus.com/PT/EC) (EC). These Natural Numbers are without dimensions or labels. The salient importance of these Natural Numbers is that they arise from Nature. Until the Proof of One (www.CQthus.com/PT/PoO), derived from the Elliptical Constant (www.CQthus.com/PT/EC), there has never been a direct relationship of numbers, thus mathematics, to Nature.

That is, basically, why Gödel contended, erroneously, that mathematics was unprovable.

Is there an algebraic function which allows us to use these new numbers?You have the horse before the cart.

How are numbers related to one another using SIS (salient intrinsic structures)?The numbers are all multiples of the Elliptical Constant (www.CQthus.com/PT/EC), (EC) which is established by any ellipse.

What other interesting properties are found with these numbers? In what ways are they useful?What can be more interesting than the Proof of One (www.CQthus.com/PT/PoO), the completeness of Gödel's Incompleteness Theory (www.CQthus.com/PT/GIT) (GIT).

These numbers also explain why the ubiquity of the Golden Ratio (www.CQthus.com/PT/GR), the Fibonacci Sequence (www.CQthus.com/PT/rFS), and elliptical motion in Nature.

In what ways are they useful? In what ways can this number system have advantages over already existing (base n) systems?There would be no number systems without Natural Numbers. All bases are contrivances of convenience.