2 + 2 = 5

The question of "2+2" is incomplete. You must always state what you are adding. Is it pineapples, average temperatures or even the speed of light.

In the case of speed of light: '1+1=1' 🙂

That's why all my math teachers would most likely take points from math tests where the answer would be simply 'x=+-1' instead of 'S={-1,1} in R'

Therefore, if you had stated objectively that you wanted to add two numbers on the realm of integers, then the obvious answer would be '2+2=4'.

However, since you have never objectively stated that, both operands could be just about anything.

Thus, it would be possible to have something called '2' that when added would result in something called '5'. As you said it yourself, we want to anthropomorphize things such as these.

Let's say the '2's were indexes of the following list: { 1, 2, 2.5, 3, 4} and that we are indexing the list from 0..n. Then you would have that the sum of two values from the list which have the index 2 would be 5.

Of course we would never write it as '2+2' in any computer language. Instead it would be written like: 'list[2] + list[2] = 5.

That's why computer languages such as Java make you declare your variables in a specific realm.

int a = 2;
int b = 2;
int c = a + b;

System.out.println("a+b=" + String.valueOf(c));
System.out.println("2+2=" + String.valueOf(2 + 2));

--> this will produce: 
a+b=4
2+2=4

And by convention any number will always be interpreted in the realm integers.

Arguably, the plus sign should indicate simple addition to most of us.

But, you could also state that the symbol '+' could also mean some complex formula like:

+ --> f(x,y)=x+y+1

That would mean you would get '2+2=5'.

Again, no one would write a problem like that expecting others would know that '+' is a math function instead of simple math addition. Therefore, we always consider by convention that the symbol '+' is the simple math addition of two operands - without even stating it as it would be too obvious (not for LLMs).

I wonder why does this look like one of those math memes we see all the time on Facebook where they ask you to guess the value of a cat by showing you the addition of ducks, bananas and cats. Or those math problems related PEMDAS where they omit all the parentheses in a simple calculation like '1+2/4'. Any serious programmer would never omit parenthesis on computer programs, thus would never allow PEMDAS to take over the real logic for their formulas.

Best regards,
Ivan