We are a part of a circle
It’s like a Mobius strip
And it goes ‘round and ‘round
Until it loses a link
Sometime between the fifth and sixth centuries B.C., the Greeks discovered infinity. The concept was so overwhelming, so bizarre, so contrary to every human intuition, that it confounded the ancient philosophers and mathematicians who discovered it, causing pain, insanity, and at least one murder. The consequences of the discovery would have profound affects on the worlds of science, mathematics, philosophy, and religion two-and-a-half millennia later.
Infinity is today so well integrated into today's language that we can scarcely imagine many thoughts and expressions without it. However, despite its widespread use, infinity is one of those objects we scarcely understand. Most of us view time as infinite and space as infinitesimally decomposable and possibly infinite,, even though both involve unmeasurable, unfathomable dimensions that defy comprehension. Yet, infinities (yes, there are several) are very, very useful to "tie" things together, to provide comprehensible models, and for the mathematician to provide a completion of mathematical theories that actually simplifies statements, proofs, and applications.
But what is infinity? How can something infinite expand? Once and for all, how can we conclude that the universe is infinite? The fact that the universe is infinite may contradict Brane theory. Consequently, could it be tenable to suggest that this Brane is a sub-universe?
Anyhow, infinity is paradoxical because something infinite is not supposed to be able to expand,.since it already goes on forever and on top of that it supposedly never ends,.
There's a fundamental bit of foolishness that underlies all of the flames. Infinity is not a number. It's a mathematical concept related to numbers, but it is not, not a number.
The structure of a fractal object is reiterated in its magnifications. Fractals can be magnified indefinitely without losing their structure and becoming "smooth"; they have an infinite perimeter, an infinite surface area. An example for a fractal curve of infinite length is the Koch snowflake.
Achilles is in a footrace with a tortoise. He allows the tortoise a head start of 100 feet. If we suppose that each racer runs at a constant speed (the tortoise slower than Aquiles), then after some time, Achilles will have run 100 feet, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say,10 feet. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.
A Möebius strip is a two-dimensional surface with the puzzling property of having only one side. Despite this mind-bending characteristic, it's an easy object to make: just take a long strip of paper, give one end a half-twist, and tape the two ends together. Because of the half-twist, the front side of one end of the strip joins with the reverse side of the other end, so that the taped-together band has only one side. This is the symbol that represent infinity.