Meta-number

A meta-number is an object like a number – in that it appears to be the answer to an equation or geometric problem – but goes beyond the confines of our universe and is unrealizable. This area of mathematics is severely under-researched, and we do not yet have the beginnings of an outline. The situation is analagous to that of astronomy several hundred years ago, where everything in the sky was called a 'star', and the modern separation of planets, star, galaxies, and even larger objects was not yet understood. Current vocabulary by Set Theoretical mathematicians include


 * Normal numbers : numbers for which the distribution of all conceivable patterns are equally distributed
 * Computable numbers : numbers for which there exists an algorithm for generating more digits of the numbers
 * transcendental numbers : numbers which can only be produced by infinite processes
 * algebraic numbers : numbers which are the solutions to finite polynomial equations
 * constructable numbers: numbers which the Greek would've recognized as able to be produced with ruler and compass only
 * infinite series : numbers which are the sums of ever decreasing amounts, so they approach an ever-narrowing range

Examples
All of the examples of what we are calling meta-numbers are what modern math calls 'irrational numbers'. We are unsure how to differentiate among them, as they may be similar or highly disparate items.


 * pi : the ratio of square of the radius to the area of circle or the ratio of twice the radius to the circumference is not a demonstrable number. There are many sequences and products which seem to approach it, however.  While there is agreement about what the first trillion digits of it look like, there is infinite more work to go to demonstrate it, where it an actual number.  Practical engineering values for it were achieved millennia ago, such as 355/113.  It appears to be normal, computable, and transcendental.


 * surds : These arose we attempted to computer distances, which is the same as solving quadratics.