Do numbers end?

Question

Is there such thing as infinidy?

Answer 1

No, here's proof.
1) take the largest number you know, add one to it.
2) now take that new number and add one to that
3) repeat steps 1 and 2 forever

Answer 2

yes, there such a thing as infinity...but you shouldnt look at infinity as a number...but more as a really really big number...not necessairily defined.

infinity is truely used to mean unboundedness....or in other words, that numbers dont have an end...no bound...thus unbounded.

for example...if you were to give me what you believed to be the biggest number, i could add 1 to it, and i would have a bigger number...you would counter and add 1 to that....and repeat the process...

so no, numbers dont end, but infinity is used to indicate really big numbers

Answer 3

No they don't and yes there is. But it's spelled infinity. As in infinite. Infinite is the idea of never ending. Numbers can't stop because you can always add something to it. After you get over a certain point thedre just isn't names for them anymore.

Answer 4

No, numbers do not end. Although infinity is sometimes thought of as the largest number, it is not. Infinity means "without end."

The following link explains infinity, if you are interested.

http://en.wikipedia.org/wiki/Infinity

Answer 5

there is no last number and just because you can't count all the way until the last number is doesn't mean that numbers do end if that part confuse you.

Answer 6

Remember that numbers are inventions that let you use math to solve problems. In school before calculus, you probably learn about natural numbers, whole numbers, integers, rational numbers, and real numbers. None of these sets of numbers has "infinity" as an element. However, in higher mathematics, it turns out to be convenient to treat infinity as a number.

For counting numbers, the greek symbol lower case omega is often used as the number that is larger than every other counting number.

In the real numbers, thought of as layed out in a line with the negative numbers on the left and the positive numbers on the right, one can define a "positive" infinity and a "negative" infinity. If you combine these two with real numbers you get the "extended real numbers." These are often represented as the "sideways eight" symbol prefixed with either a + or a -.

Complex numbers are arranged in a plane, so if there is an infinity it doesn't lie in just one direction, but "all around the edges" of the infinite plane. One way to manage this is to imagine the complex numbers arranged around a sphere. Imagine the complex numbers first layed out "on the ground" in an infinite plane. Then set a sphere with its south pole touching the origin of the plane to the bottom of the sphere. The north pole of the sphere is on the top side of the sphere. Every point on the plane can be associated with a corresponding point on the sphere with the steps outlined below.

Pick a point on the complex number plane, draw a line in 3d space from the north pole of the sphere to the given complex number in the plane. That line will pass through exactly one point on the surface of the sphere. That point on the surface is the "spherical" representation of the complex number. The further out the number is from the origin on the plane, the higher up the number is on the sphere. The "natural" place to represent infinity as a complex number, then, is in the "spherical" representation at the north pole of the sphere.

Things can even get wilder in the "counting" case, as you might study in amy good book on set theory. One way to think about counting is that you are matching sizes of sets. The normal way to do this is establish a "mapping" between the two sets, one whose size you know and the other whose size you want to measure. That's what you do when you start pointing at the oreos in your lunch and start reciting the numbers "1, 2, 3" etc.

In the "extended counting numbers", we get from one number to the next by adding one, except for infinity--it doesn't come from adding one to anything but it is greater than all the numbers. Then if you discover a set where you can match any of the counting numbers to exactly one element of your set, you say that the set has a size, or "cardinality" of little omega.

Of course, if you think of this infinity as a number, then you can add one to it and get "little omega" +1, followed by "little omega" + 2, and get a whole other range of numbers bigger than "little omega". You could then think of a smallest "infinite" number that is still bigger than "little omega" + k for any natural number k but not the "next" number after any of them. It would be natural to call this 2 "little omega". In this way you can construct 3 infinity, then 4 infinity, etc. It turns out that you can setup a "mapping from any of these "large" looking infinities back to "little omega", so even though it seems like you've added lots of bigger infinities, you really haven't created anything with a larger cardinality.

But, if turns out that you can get a set that is so big that you can't match it up exactly one-to-one with the elements of the natural numbers. The rational numbers seem to be a large set, but not large enough to have a bigger cardinality than the natural numbers. However, the way real numbers are defined, there is no way to match up every real number with the natural numbers exactly one-for-one. So, you eventually need a number that represents the smallest number that is not the successor of any smaller number and that the size of the set of numbers smaller than it is too big to be counted with the counting numbers. This is the "first uncountable number" and is often represented as "capital omega".

To represent the size of the infinite sets, you may also see the notation using the Hebrew letter "aleph" with a subscript. "Aleph zero" corresponds to the cardinality of the set of numbers less than "little omega" above--the size of the set of all natural numbers. "Aleph one" corresponds to the cardinality of the set of numbers less than "capital omega"--the size of the set of all real numbers. As you might imagine, you can construct sets that have a cardinality bigger than any "aleph k" you might have, although it becomes increasingly difficult to cook up examples. If I remember right, the set of all the curves in the plane have a cardinality of "aleph 2".

So, the answer to your question from a set theory point of view, is that there is no reason to limit the size of a set. Not only is there an infinity, but there is a whole family of infinities of ever increasing sizes!

Answer 7

No