how much is infinity???

Answer 1

Infinity is any large number one cares to name. Just remember that anyone else can name a number even larger by just adding one to it. The American Heritage Dictionary, Second College Edition, defines infinity as "an indefinitely large number." For that reason, infinity cannot be fixed numerically.

Answer 2

Imagine you had a cup of sugar

You are going to empty the cup by removing the sugar at a rate of 0 (zero) grains at a time. Well infinity is the time it takes to empty that cup with no other sugar losses of any kind from the cup.

Imagine you had a line segment 2 inches long. You are going to remove that line segment by removing 1 point at a time and naming them by the distance they are from one end of that line segment. Infinity is the number of named points you would have if you were able to finish the task

Imagine you were a point moving at a finite and positive speed along the positive arm of the hyperbola y = 1/x from the point (1, 1) in the positive x direction. Well infinity is the time it will take you to reach the x-axis

As you can see, infinity is very very large ... so large we cannot express it as a number ... just a symbol namely ∞

Answer 3

Everyone that has learned to count knows that there is no end to counting. There is no last number.

But yet, we speak of all the positive integers.
It's as if we can put all the positive integers in a box and pick up that box.

On one hand we have boxed in the positive integers.
On the other hand we know that we cannot name all of them.

We express the notion that we could count forever without naming all the positive integers

by saying that the number of positive integers is infinite.

So this particular infinity, the infinity of the number of positive integers is not a positive integer, but we think of it as greater than every positive integer.

I'll let this be my answer for now. I'll save the discussion of the other infinities for another question.

Answer 4

In mathematics there are different 'infinities' or rather different sets of infinite size but which have different numbers of things in them... I know ... it's a bit mind boggling.

e.g. the number of counting numbers 1,2,3,4 .... is infinite and the same size as the infinite number of even numbers. The number of all of the possible fractions of the form n/m (1/2, 1,3, 2/3, ... 71/117 ...) is actually the same size as well. But the number of possible decimal fractions between 0 and 1 is bigger than any of them ...

You can take a look here for a good basic introduction:
http://scidiv.bcc.ctc.edu/Math/infinity.html

You can try wikipedia
http://en.wikipedia.org/wiki/Aleph_number for a more formal discussion of Aleph numbers.

Or you can try

"The Mystery of the Aleph: Mathematics, the Kabbalah and the Search for Infinity"
by Amir D. Aczel

which has a pretty readable account of this subject.

Answer 5

I will try to give u an idea of infinity.
When a black hole is formed u will find that it is in the center of a Galaxy. The mass that holds everything in orbit around produces a gravity well that may be 5 light years across . That is a definition by nature of how big infinite is.

Answer 6

There are different ways to discribe infinite. There is countably infinite and uncountably infinite. Something is countably infinite if there is a 1-1 and onto function from the natural numbers to the set. Rational numbers, natural numbers, integers, odd numbers, even numbers, etc. are countably infinite. The cardinality (number of elements) in this set is something called aleph-0. Something that is not uncountably infinite is like all the numbers between 0 and 1. The cardinality of this set is c. My most recent math class defined infinite as not finite, at that point we laughed at the teacher, but it is the mathematical definition. For something to be finite it has to be countable, and you have to be able to find the stopping place.

Answer 7

Infinity is not a value or number, but more like a concept. It is just the simple idea that a number or value will continue growing bigger without stop.

Answer 8

1. Engineering/computing approach: For practical everyday reasons a number big enough to make a function definable even if not always computable.

E.g. With infinite time we can enumerate all positions on a chess board.
E.g. After playing a die infinite times the number of 1s / number of plays = 1/6
E.g. The value of (n^2+n)/(2·n^2) when n is infinite = 1/2.

Curiosity: Any astronomical example is very small (there are "only" 10^80 particles in the universe) in comparison with everyday combinatorial problems (e.g. cryptographic security of Internet transmissions or the number of legal positions in the game of go.)

This practical definition is very intuitive, it behaves as a very big number (where the definition of big changes from one problem to another).

2. Pure mathematical approach: The infinite (aleph zero) is the cardinal (number of elements) of the set of the natural numbers. This notion is harder to grasp because it is founded on set theory. Mathematics is itself based of set theory (usually referred to as ZFC).
It has counter intuitive ideas:
E.g. There is the same number of integers and even numbers.
That contradicts common sense since all even numbers are integers and there are also odd numbers which are integers and not even. That common sense reasoning is valid for any size of *finite* sets, but it is not valid for infinite sets. In infinite sets, what counts is that we can define a one-to-one relation between both sets. e=2*i Each element of the integers (i) has a unique image in the set of the even numbers (its double) and each element in the even numbers (e) has a unique image in the set of the integers (its half). Therefore, both sets have the same number of elements which is infinite (the smallest known infinite) called aleph zero. There are also higher level infinites, as the cardinal of the real numbers which is not countable.

This looks as a paradox, but it is perfectly sound reasoning and a cornerstone of mathematics. Without understanding infinite you cannot really understand numbers, functional analysis or any high level math.

Answer 9

infinity= no limit

Answer 10

ınfinity times zeroes exist in any real number