What is meant by infinity? What phenomena in the universe is infinite? Is the term just a mathematical construct, or is there evidence that there is a basis in actual reality? Infinity and the infinite have confounded humans since time immemorial. Has modern science gained any more knowledge to this concept?
At an intuitive level, the infinite comprises that which is larger than any magnitude that can be counted or imagined. In mathematics, the set of real numbers, prime numbers, the number pi, the numbers between 1 and 0 all comprise of an infinity of elements. If infinity is loosely defined as something bigger than any finite number, then correspondingly, the "infinitesimal" is something which is not zero, but smaller than any non-zero number. Eventually mathematicians considered the infinitesimal and infinity as not real numbers as such, but processes.
Consider the statement:
When a mathematician writes 1/0 = infinity, it doesn't mean we should take this equation literally. What it means is that as "x" keeps shrinking closer to zero, approaching zero, then 1/x keeps growing bigger approaching infinity.
New Scientist, No. 2414, 27 September 2003 - Special Issue on Infinity.
Infinity in reality?
An infinity of reflecting surfaces ... an illusion certainly, whether generated by mirrors, tricks of the light or by other means. From a starting point (if there is any), and vanishing to infinity. Can such images be a metaphor for the continuity of life in all its manifestations throughout time and space?
Some mathematicians consider in the vastness of theory that there exists multiple sets of infinities - each extending onwards, outwards or inwards forever and never coming to an end or finality. More complex questions arise when one starts to do calculations with infinity, such as when infinity is multiplied by another infinity, or raised to a power of an infinity.
How can one contemplate infinity? How can such a purely abstract concept have any meaning in the real world? In geometry, a triangle of infinite length becomes the paradox whereby parallel lines can meet at a point situated at infinity. A circle can be considered to be a ploygon made up of an infinite number of sides, similarly, a sphere can be considered the result of an infinite number of facets. Fractal geometry best illustrates that an object can contain within its boundaries an infinite degree of complexity no matter how much one magnifies the image. The famous Mandelbrot Set has within its internal geometry an infinite amount of detail extending further and further to the recesses of infinity.
No matter how one magnifies the image of the Mandelbrot Set, contained within the structure is an infinite amount of detail. It is both beautiful and intriguing. Far more complex than anything the imagination could behold.
The concepts of zero and infinity are the outer limits from which reality emerges. All real numbers and geometrical constructs exist within the domain framed by the infinite.