Reddit reviews The Mathematics of Infinity: A Guide to Great Ideas

Yes, googling things is not a rigorous way of approaching the topic. But also, the first response agrees with what I'm saying. In fact, if you actually look at the accepted answer of the stack exchange question you found, you will see they also agree with me.

https://math.stackexchange.com/questions/596028/does-cardinality-really-have-something-to-do-with-the-number-of-elements-in-a-in


> What is a number? It is an informal notion of a measurement of size. This size can be discrete, like the integers, or a ratio, or length (like the real numbers) and so on.

> Cardinal numbers, and the notion of cardinality, can be seen as a very good notion for the size of sets.
>
> One can talk about other ways of describing the size of an infinite set. But cardinality is a very good notion because it doesn't require additional structure to be put on the set. For example, it's very easy to see how to define a bijection between ℕ
> and ℤ
>
> , but as ordered sets these are nothing alike. Cardinality allows us to discard that structure.
>
> Once accepting this as a reasonable notion for the size of a set, we can now say that the number of elements a set has is its cardinality.


But none of that matters, here is a excerpt from an actually rigorous book on the topic.

https://i.imgur.com/8IUGcYa.png

Just to note:

>The cardinality of a set X is a way of measuring in precise mathematical terms the number of elements in X.

Go read any math book on these topics and you will see unanimous agreement with this point. This is a mathematical statement that has been proven for well over 100 years.