Is infinity bigger than infinity+1?
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Infinity is a concept that has a lot of ways to be defined properly. There is the easy solution of saying that “infinity+1 doesn’t exists”, but with a good number of definitions of infinity we can actually define “infinity+1”.
So, how does “Infinity+1” works? First let’s agree on which infinite number we select here. Infinite numbers are called **ordinals**. In our case, we take what is called the **countable** infinity. That’s the one you obtain when you do 1, 2, 3, etc, “Infinity”.
* “Infinity+1” is of exactly the **same size** as “Infinity” (or of the **same cardinality**, if you want to use the dedicated mathematical term). There are bigger ordinals than that. in particular the **continuous infinity** is bigger than both “Infinity” and “Infinity+1”, but that’s another subject.
* “Infinity+1” as in “Infinity and we add an element at the end” is a **greater** ordinal than “Infinity”. In some ways, you can say that “Infinity+1” is **bigger by a negligible amount** than “Infinity”, which mean that if you look at how they are ordered, “Infinity+1” comes after “Infinity”, but if you look at their size then they both have the same size.
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