Please tell me about infinity.?

Answer 1

In mathematics, the word "infinity" by itself is seldom used and difficult to define. It is the value that is beyond all finite values.

If a point has size zero (as on the line of real numbers), then the number of points on the line is infinite.

What is defined is a finite value: any quantity that is bounded. A bound is a number that is either above the value (upper bound) or below the number (lower bound).

For example, pi cannot be written as a rational number (fractions involving integers). However you can find an upper bound (for example 22/7) and a lower bound (6,283/20,000).

You can get these bounds as close to the number as you want, depending on the accuracy you need.

A number that is "so big" that you cannot find an upper bound is called "boundless". Because it does not allow a bound, it is not a finite number: therefore it is infinite (not finite).

In arithmetic, this number we call infinity does not exist. In most branches of math, you can "tend to infinity" or have a limit at infinity, but you cannot have a number that is "infinity".

In some other branches, you can (like in the complex field).

In set theory, there may even be levels of infinity.

Strange things happen when you do operations involving infinity.

For example, take the list of all positive numbers:

1, 2, 3, 4...
How many are there? The number of numbers is not finite. For any number N that I would offer as an upper bound, all you have to do is show me that N+1 is a number.
So, we say that the number of numbers is infinite.

Now, take the same list, and multiply all the numbers by 2. You get 2, 4, 6, 8, 10...
How many even numbers are there? Obviously the same number as all the numbers since all you did is multiply each of the original numbers by 2. Call this list E (for Even).

Now, let us create another list by subtracting one to each number of list E. We get
1, 3, 5, 7, 9... How many of them? The same number as we had in list E, which is the same number as we had in our original list. Let us call this list O (for Odd).

Let us put together lists E and list O to get:
1, 2, 3, 4, ...

We have put together two lists, each of which had the same number of numbers as the original list; should we not have twice the number of numbers than in our original list?

That is what we get for adding "infinities"

Answer 2

The problem with infinity is that it can't be conceptualized. Here's an example:

Are you familiar with the Mandelbrot set (see http://en.wikipedia.org/wiki/Mandelbrot_set)? OK. There are an infinite number of points in the set. But at each point in the Mandelbrot set there is another set of points called a Julia set (see the same Wiki article). And there are an infinite number of points in a Julia set.

Now all of a sudden you have an infinity of infinities. But it's still only infinity. Infinity didn't get any larger and there is no such thing as infinity squared (which would be implied by the above). It's just infinity.

Got that?

Answer 3

It is either very big, or very small, as something can be infinitely small. Infinity deals with the endless and the boundless. Take a big number. Then double it. Then double that number again. And again. And again. Perpetually. It will get huge, but it is not until an infinite amount of time that this number would be infinite.
It is a difficult concept to grasp because we are finite, and everything we can experience is also finite. You need to grasp infinity to understand infinity, and that is a hard thing to do, perhaps infinitely difficult...

Answer 4

Just consider that as the biggest number you know. So it will make sense when you divide infinity by one you will get infinity. If you divide 1 by infinity you will get 0. 00000000000goes on, which is 0

Answer 5

There is no such thing as infinity. It is merely a concept used to ease the insecurities of enquiring minds when attempting to model the universe around us. We live in a finite universe, and infinity is as alien to that universe as the square root of a negative number. True it serves as a useful tool in it's idealogical form, but it can never be realised, you can never grasp it or touch it. Accept it for what it is, a handy spanner in the physical or mathematical toolbox, but don't try to explain it. That way lies religion.

Answer 6

In mathematics, infinity is not a number, but rather an idea.The idea is that some things in mathematics go on forever without end. Forexample, the number line goes on for infinity: there is no largest number. Likewise in the negative direction, there is no smallest number: negative numbers go on for infinity, also

Certain mathematical operations never end also. An example here is 100/3=33.33333333333333333333333333333333333333333333...forever without end, for infinity.

Get it?

:)

Answer 7

think of the graph y = 1/x

as x approaches +0 y appears to continue up to infinity. and also as x approaches -0 y appears to continue down to negative infinity. this also proves that division by 0 is impossible

Answer 8

It's really big.

You might read the book
"One, Two, Three... Infinity" by George Gamow.
Very good description

He tells a story about the "Infinite Hotel", that has an infinite number of rooms.

An infinite number of guests show up, and they are each given a room. You might think the hotel is full...

One more guest comes in, and the manager asks the person in room 1 to move to room 2, the person in room 2 to move to room 3, etc. The new guest is given room 1.

An infinite number of new guests show up. The manager asks the person in room 1 to move to room 2, the person in room 2 to move to room 4, etc. Now all the odd numbered rooms are empty, and he puts the new crowd in those.

There is always room in the Infinite Hotel.

Answer 9

A teacher once told me:

Imagine a block of granite the size of the universe. Once every million years, a sparrow comes along a pecks a single grain out of the granite block. When that entire block has been pecked away, that is only the beginning of infinity.

Answer 10

Infinity is not a number. It is a symbol which means "more than every number you choose".