Are all infinities the same?
The term infinity can refer to multiple concepts that, although related, are mathematically defined differently.

Infinity is commonly imagined as a point that something can travel towards but never visit. An example of this is the idea of positive and negative infinity on the real number line.

Infinity can also refer to sizes, such as the amount of all real numbers, or the amount of integers. Georg Cantor proved that there are an infinite amount of these infinities. These infinities are called cardinal and ordinal numbers. For instance, the cardinality of the rational numbers is the same as the cardinality of the integers (in the sense that each integer can be paired with one rational number without skipping or repeating rational numbers). However, the cardinality of the real numbers is not the same as the cardinality of the rational numbers.
yes