Infinity

Infinity is something without bounds that goes on forever. But in

mathematics, infinity can be defined as any real number larger  9.9 ×1099.

So how do we grasp the concept of infinity? Stand between 2 mirrors

and you would see your image go on an infinity number of times (it never

ends).

The concept of infinity was first conceived by the Greeks to explain

limitlessness. Also the Hindus used it for their creation story when they

said there are limitless number of creators thus they don't know the

first one.

There is something funny about infinity: some

infinity are greater than others! How many real numbers are between 0 and

1? The answer is infinity. How? We have 0.1, 0.01,0.001,

0.0001,.....0.2, 0.21, 0.22,... If you count all the real numbers

between, they are greater than  9.9 ×1099. Now how many real numbers

are between 0 and 2 ? It's also infinity but surely it is greater than

the first infinity.

This has been exploited in cosmology. If we are to measure the

radius of the universe in femto meters (1015), we might be

approaching a value close to infinity but if measured in light years

(9.64 ×1015 ) we would get a value far from infinity. So to avoid

saying infinity femto meters (which is not an actual value) we say

100,000,000 light years which is finite.

PARADOX:

Infinity has been used to formulate several paradoxes; for example:

1. Hilbert's paradox of the Grand Hotel.

“So,” this asks, “is it possible to fill a ‘Grand

Hotel’ which has an infinite number of

rooms, with an infinite number of guests?”

Well, I for one do not know. Let's say you can.

What then happens when a new guest

arrives? 

There are an infinite number of rooms,                                                                                        so obviously, the guest will find a room.

But if he finds a room, then the hotel was

never filled in the first place, although it is said that

there are an infinite number of guests, so

why can't they fill it?

2. The Library of Babel.

In this library exists every name ever given

or will ever be given, every sentence ever

said or that will ever be said. The library

works by generating an infinite combination

of the 26 letters of the English language and

the characters "." , '','' and space. It can be found here

and has about 105000 characters. Compare

that to the number of atoms in the universe

and...

3. Zeno's paradox

Ahh, this old one. This simply states that if we

have two points, A and B, and you wanted to

go from A to B, you would have to first pass

half of that distance. But, damn, in order to get

to that half, you need to get to HALF of the

first half . . . and so on and so forth. that at

the end, you shouldn't even be moving.

There are other fascinating concepts of infinity like the value of pi.

-Valentine O.

Gfaze Team