Infinity+Mathematics

In Omnia, Infinity to the power of infinity haz the value uv an infinite number of relative classes, each with an infinite number of members in an infinite existence eternally computed by the All Mind. = = =[|What Is Infinity in Math?]=

By Kathryn White, eHow Contributor

Some calculations with infinity are possible. The idea of infinity has boggled the mind for centuries. Indeed, it sometimes seems almost impossible to comprehend. Yet over the centuries, philosophers and mathematicians have come up with systems for expressing and referring to infinity in math. Although even young children might ponder the concept of infinity in abstract terms, higher-level math __ courses __ such as calculus require a more in-depth comprehension and use of the term. Read more: [|What Is Infinity in Math? | eHow.com] [|http://www.ehow.com/about_6460119_infinity-math_.html#ixzz1r6pcnVv8]

History
> In the centuries that followed, mathematicians disagreed about the distinction between a potential infinity (which could exist) and an actual infinity (which does exist), until George Cantor finally showed that these two were one and the same.
 * Early mathematicians, such as those in ancient Greece, concerned themselves with the practical application of __ math __. Although they recognized the idea of infinity, they hesitated to explore it because they thought it had no practical purpose. Furthermore, these ancients did not have the algebraic skills to work with the idea, says Dina Gohar, author of "Cantor's Quest to Understand the Infinite."

Representions

 * In math, it is possible to represent the concept of infinity in several ways. For instance, an ellipse expresses the idea that a set of numbers continues on forever unbroken--for instance (-2, -1, -3...). In addition, the arrows used for the ends of graphs on the coordinate plane show that the lines, and the mathematical relationships for which they stand, remain true for an infinite number of coordinate pairs. This particular representation can be used to visually determine or express a limit as a variable approaches an asymptote. For example, if the graph contains an asymptote at x = 3, the arrows on the graph near the asymptote would show that y continues on infinitely in either a positive or negative direction.

The Symbol

 * Although there are numerous ways to represent the idea of infinity, John Wallis (1616-1703) came up with the particular symbol used as a notation for infinity. This symbol looks like a sideways figure eight and is drawn like this: ∞. Infinity can be positive, in which case the symbol is drawn with a plus sign: +∞. Or it can be negative, drawn with a negative sign: - ∞.

Multiplication and Addition
> Likewise, - ∞ X - ∞ = ∞, because a negative times a negative equals a positive. Negative infinity times positive infinity equals negative infinity, and negative infinity plus negative infinity equals a very negative number--negative infinity.
 * It might seem impossible to do operations with infinity in math without actual values, but certain ones can be expressed using common sense. For example, ∞ x ∞ = ∞ because, even though the actual numerical value of infinity is unknown, we do know that it is an extremely large number, and an extremely large number repeated an extremely large number of times will always give an extremely large number. Infinity plus infinity also equals infinity for the same reason.

Division and Subtraction

 * A real number divided by infinity (e.g. 3/∞) equals zero because a small known number divided by a huge number approaches zero. Yet, ∞/∞ is considered indeterminate because the answer would probably be some smaller number that is impossible to determine. The same goes for ∞ - ∞; it is also considered indeterminate. Any answers to these indeterminate operations with infinity depend on how the specific problem with infinity is defined.

Read more: [|What Is Infinity in Math? | eHow.com] [|http://www.ehow.com/about_6460119_infinity-math_.html#ixzz1r6qZKrE2]