No, infinity times 2 is not bigger than infinity.
Infinity is not a number in the traditional sense but rather a concept representing something without any limit. Because it's not a number, standard arithmetic operations don't always apply as we might expect.
Here's a breakdown:
- Infinity is a Concept: It represents a quantity that goes on without bound.
- Multiplication Doesn't Change Infinity: As the reference indicates, infinity multiplied by any constant (other than 0) is still infinity.
To understand why, consider different "sizes" of infinity. For example:
- The infinity of all natural numbers (1, 2, 3, ...)
- The infinity of all real numbers (which includes fractions, irrational numbers, etc.)
The infinity of all real numbers is larger than the infinity of all natural numbers. However, multiplying the set of natural numbers by 2, for example, does not change the size of its infinity; we simply have two sets of natural numbers. Each set has the same cardinality (or size of infinity).
Therefore, while the idea of "2 times infinity" might sound bigger, it's still ultimately representing an unbounded quantity of the same magnitude.
