what do you get when you add infinity to infinity?

Question

i.e. an infinite number to an infinite number a new infinite number???!!!!!!!!!!!!!!!!!!!!

Answer 1

You get infinity. However, there are different orders of infinity. The infinite sum will have the same order as the greatest order (or cardinality) of the infinite addends.

The number of integers is infinite, but it is "countably infinite," or "aleph-null," the lowest (or zeroth) order of infinity. This is the same as the number of rational numbers, the number of square numbers, the number of even numbers, or any subset of integers or rational numbers. However, the number of real numbers is greater. It is "aleph-one," the cardinality of a continuum. Aleph-two is the cardinality of sets of points in real Cartesian space.

Answer 2

There is more than one type of infinity, there is positive infinity as being very large and very small. there is also negitive infinity as being very large and very small also. But if you have two numbers, say 1 and 2, there is an infinite number of numbers between these two numers, so which of the 5 (I am sure you also know there is an infinite set of numbers with infinite numbers between them) do you want to add up. Infinity is the infinte amount of answers you get.

Answer 3

The first answerer really has hit the nail on the head [although I think you are wrong when you say any set of Q or Z has cardinality Aleph-Null, since {1,2} is a subset of Z but has cardinality 2].

However this takes some complex mathematics to really understand, but I'll try and explain some of the terms:

Countability. The Set of integers {...-1, 0, 1, 2 ...} is described as countable since there is an easy method of counting them. You start from zero and just add one each time, and you'll hit every single positive integer. If you subtract one each time, you'll hit ever single negative integer, you wont miss any out.

The rational numbers [fractions] are also countable because we can describe a neat way to count them all. If you remember mutiplication tables, then this table is a division table and following the path, you'll hit every single rational number:

http://deron.meranda.us/topics/infinity/rational_diagonalization.png

However there is a proof that you cannot do this for all real numbers. Some numbers are not rational, we can prove that [Sqrt2 is famously irrational, as is Pi and e]. We can also prove that there is no method for counting them like we can the integers and rationals. It's impossible to cook up a recipe that you can follow through and hit all the real numbers. This means that in some way, there are more real numbers than there are rational numbers. But there are the same amount of integers as there are rational numbers. It sounds crazy and in a way it is but trust me, its logically sound.

The above describes different orders of infinity, but its easy to conceptualise different types of infinity. For instance if I took a pencil, started at your feet and just kept on drawing away from you, you'd be at the beginning of an infnitely long line. Now if my brother did the same thing but in the opposite direction, you'd be in the "middle" of an infinitely long line which has neither beginning nor end. Intuitively this seems longer than the line I just drew, but is it really?

Since infinity is never actually used in an equation [it is nonsense to perform operations on infinity, we think of a variable x tending to infinity, meaning it just gets bigger and bigger and never stops] adding something to infninity doesn't really make sense. Conceptually though, its still infinite.

A better way to think of infinity is indefinite, meaning that it just goes on for ever. Don't try and contain infinity by thinking of it as a number. It's not.

Answer 4

Infinity + Infinity = Infinity
Infinity - Infinity is undefined
Infinity / Infinity is undefined
Infinity * Infinity = Infinity
1 / Infinity = 0
Infinity * 0 is undefined
Infinity ^ 0 = 1

Answer 5

Infinity
infinity + infinity = infinity , 1/ infinity = 0 , infinity/any number except infinity = infinity ,infinity/0=undefined, infinity/infinity = 1.

Answer 6

Infinity plus or minus any number is still infinity!

Answer 7

Infinity is not a number. It is just a concept or symbol to represent the biggest number ever imaginable. So no use adding inf to inf.

Answer 8

infinity

Answer 9

infinity is not a finite number .it is only suppose the highest number is called infinty.then you adding any number you give only highist number that's called infinity.

Answer 10

just get infinity of course