Hardest question ever ( ͡° ͜ʖ ͡°)

2

1+1 is an expression, which is equivalent to a constant value, 2.

obviously you don't know set theory

There is many kinds of infinity! Here is one:

Let's call the empty set "0"

Definition A: the "successor function" S(x) = x ∪ {x}
Definition B: a "natural number" is 0 or the successor of a number (here "natural number" should be more formally "Von Neumann Ordinal")

I define 1 to be S(0). By definition B, 1 is a natural number.
I define 2 to be S(S(0)) = S(1). By definition B, 2 is a natural number.
I define 3 to be S(S(S(0))) = S(S(1)) = S(2). By definition B, 2 is a natural number.
etc.

There exists a set "omega" define as the following:
- 0 is member of omega
- for all x, if x is member of omega, then S(x) is also member of omega

Omega can be visualized as the "limit" of 0,1,2,3,4,...,n-1,n,n+1,n+2,...

I now define "ordinal" as following:
- 0 is an ordinal
- The successor of any ordinal is an ordinal
- The limit of a sequence of ordinals is an ordinal
- If an ordinal A is a member of an ordinal B, then "B > A" and "A < B"
- Given an ordinal A and an ordinal B, if neither of them contains the other as an element, then "A = B"

Note that all non-natural-numbers ordinals are "infinite"
From there you can create ordinals such that omega-plus-one, omega-plus-two, etc until omega-times-two, omega-times-omega, and so on.

Unlimited possibilities! And it is important to know that there is _no_ largest ordinal

There is many kinds of ordinals, such as "countable ordinals", "uncountable ordinals" (e.g. ordinals that has as many elements as there is real numbers, or even more elements), (non-)recursive ordinals, admissible ordinals, etc.

"Omega" is probably what is the closest of the common idea of "infinity", but some ordinals are much, MUCH greater than tha

haha xDDD I love maths <3<3<3<3<3

21 ( ͡° ͜ʖ ͡°)