Is infinity bigger than infinity+1?
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There are different kinds of infinity. But infinity+1 is always the same size as infinity.
For example, there are an infinite number of even numbers, and an infinite number of all numbers.
Imagine taking each even number and matching it with a different natural number. 2 matches to 1, 4 to 2, 6 to 3, 8 to 4, and so on.
Now, we can never run out of numbers. We can always add 1 or 2 to make a new number. And that new number would also have a match.
Since this is the case, infinity+1 is the same size as infinity.
A scenario where two infinities aren’t the same size would be as follows…
Imagine the infinity of all natural numbers, N. And the infinity of all real numbers, R.
R is larger than N.
This is because, for real numbers, there are an infinite number of subdivisions between any two real numbers.
While not strictly true, the size of R is about the size of N squared. It’s an infinity compromised of smaller infinities.
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