# What is infinity plus infinity?

Is it 2 infinity and beyond?

### 12 Answers

- cmcsafeLv 72 months agoBest answer
Two points must be borne in mind

• Infinity is not a number so we are not allowed to apply numerical rules.

• There are an infinity of infinities all different from each other indicated by ℵ₀,ℵ₁,ℵ₂,....

Being practical, very often, we use the symbols +, -, * ... but we must pay close attention to the meaning

For example

ℵ₀+ℵ₁=ℵ₁

For example If I make the union between the set of natural numbers ℕ and the set of real number ℝ we got a set with numerical cardinality ℵ₁

but

ℵ₀+ℵ₀= ?

Could be 0. Ex. ℕ\ℕ

Could be 1. Ex ℕ\{ℕ\{0})

Could be 2.....

Could be ℵ₀ Ex. ℤ\ℕ

But never will be ℵ₁.

- JOHNLv 72 months ago
The set, U, of even numbers is infinite. The set ,V, of odd mbers is infinite. When you add them together you get the set W of all the integers, another infinite set. You can pair off any two of U V, and W one-to-one, so they are all of the same size. Thus ∞ + ∞ = ∞. But you can't pair off the integers and the real numbers one-to-one. The infinity of the integers (aleph_0) is smaller than that of the real numbers (aleph_1). aleph_0 < aleph_1.

- billrussell42Lv 72 months ago
cmc is correct. Simplifying, if you take only the lowest order of infinity, the set of numbers, then infinity+infinity = infinity.

for example, set of positive even numbers, infinity, plus set of positive odd numbers, infinity, equals set of positive numbers, infinity.

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- Geeganage WLv 52 months ago
There is no such number called infinity. Conceptually, any number beyond the imagination is taken as infinity. Suppose, any integer (not zero) is divided by infinitesimally small number "x" (where x tends to zero) the answer becomes unthinkably large and it's called infinity. If you add anything to infinity it becomes infinity and, infinity plus infinity is also infinity. Understand the concept.

- 2 months ago
It's infinity

infinity - infinity can be infinity, 0, -infinity, or anything in between

infinity/infinity can be infinity, 1, 0, etc...

Infinity doesn't behave according to intuitive rules. That is, we can conceptualize rather easily how 1 + 1 = 2 and how 1 - 1 = 0. But infinity behaves differently, depending on the situation.

- Anonymous2 months ago
Infinity. There’s nothing beyond.