What is 2 + 2?

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το μουνί της μάνας σου.

An expression

1+1 + 1+1

[math]
\text{ }^{\color{#571da2}{\displaystyle\text{W}}}\text{ }^{^{^{^{\color{#462eb9}{\displaystyle\text{h}}}}}}\text{ }^{^{^{^{^{^{^{\color{#3f47c8}{\displaystyle\text{y}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{\color{#3f62cf}{\displaystyle\text{ }}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#437ccc}{\displaystyle\text{i}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#4b90bf}{\displaystyle\text{s}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#56a0ae}{\displaystyle\text{ }}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#62ab99}{\displaystyle\text{t}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#71b484}{\displaystyle\text{h}}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#82ba70}{\displaystyle\text{i}}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#96bc5f}{\displaystyle\text{s}}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#a9bd52}{\displaystyle\text{ }}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#bcbb48}{\displaystyle\text{o}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#ceb541}{\displaystyle\text{n}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#dcab3c}{\displaystyle\text{ }}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#e39938}{\displaystyle\text{/}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{\color{#e68033}{\displaystyle\text{s}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{\color{#e3632d}{\displaystyle\text{c}}}}}}}}}\text{ }^{^{^{^{\color{#de4227}{\displaystyle\text{i}}}}}}\text{ }^{\color{#da2121}{\displaystyle\text{/}}}
[/math]

That is a very interesting question. In Wildberger's latest video he discusses how we don't actually have a solid theory that links our numbers with the expressions we can construct from those numbers.

For example, we may be able to say 2+2=4 but what are we really saying? That in any context we can replace 4 with 2+2 and that will be fine?

Is this correct? Do we have a solid theory that justifies this to be true for every possible expression? Is there any proof that shows that with all the known operators, there exists one and only one number that can be said to be equal to any expression no matter how complex or long or even ridiculous?

Honestly, we don't know. We don't have that theory and we may not have it for hundreds of years. Knowing that, is it then even fair to say 2+2=4?

No, it isn't. If we don't know the limits of our system then is it logical to assume that even something as simple as 2+2 does not break those unknown limits? It isn't because we don't know.

We may be able to conjecture that 2+2=4 is a trivial equality and that no limits are being broken but we can't prove it because we do not know the limit of our expressions. Where can we go? Where does it end? We don't know.

We don't know.

Your mom

εισαι ο πρωτος ελληνας που βρηkα σ'αυτο το board

Whether of not expressions in a system reduce to a particular normal form is well studied

en.wikipedia.org/wiki/Confluence_(abstract_rewriting)

Χωρίς σημαίες είναι kαι δύσkολο να kαταλάβεις με ποιον μιλάς. Και εγώ δεν νομίζω να έχω πετύχει kάποιον άλλον εδώ.