Infinity equals Infinity ..... or does it?

Question

Shouldn't there be twice as many whole numbers (even and odd)
as there are just the even whole numbers?

Count even numbers (2, 4, 6, 8 ... ) = infinity.
Count whole numbers (1, 2, 3, 4 ...) = infinity

Infinity = Infinity ..... or does it?

Answer 1

In upper division maths you learn about different degrees of infinity. How one infinity might be different or larger then another. So your sum of even numbers will be twice as large as the sum of your whole numbers if taken with absolute values.

Just think like 1 / (sum of all whole numbers). That doesnt neccesserly go towards infinity, it keeps going but it apporaches a number. (1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 ... 1/x) where x -> infinity.
1/x is going to approach 0. so you will have a really good estimat e if you just added your first 20 numbers. You will learn the rest of this in calculus.

Answer 2

indeed there is no such thing as diffrent infinity, the patterns described above run infinite but the rate of infinity, or towards infinity can be different. Sat 1+1=2+1=3+1 but 2+4=6+2 is going +1 faster always in terms of rate as such count even numbers are reaching towards infinity faster

Answer 3

infinity is not a number. It is a concept only. Anyway, I want to answer this question by an question. "Which infinity?" 5/0 or 6/0 ? Which infinity did you mean? Although, concepts don't have any numeric values. they can't be equated.

Answer 4

Infinity is infinity. No numbers included. What you are referring to is etc. Infinity is just explained as endless. A destination to say. I guess it all depends how you view infinity. Like space for example. We can go as 2 or go alone as one. But the destination is still the same. Infinity.

Answer 5

The two sets aren't equal but have the same cardinality i.e. exists a bijection among the two sets

P= the set of even numbers
N=the sets of natural numbers

f: N -> P with f(n)=2n is a bijection

Not all infinite sets have the same cardinality.

e.g. R= the set of all real numbers has the cardinality of continuum which is greater than the countable cardinality

One possible definition of infinite set is:
a set which has the same cardinality of an its own proper subset.

Sorry for my english.

Answer 6

It can be shown that there are just as many even numbers as whole numbers: for every whole number n, there is an even number n * 2.

In other words, the cardinalities of the two sets are both aleph null.

Answer 7

No. There are "orders of infinity" as first described by George Cantor in 1870.

Aloha

Answer 8

You are assuming that infinity means a figure you can reach. If that were true it would be finite, not infinite.

Answer 9

Infinitey is infinity.....by definition...

Answer 10

infinity=infinity. its reflexive. or whatever its called. ;).