Prove to me that 1+1=2

Prove to me that 1+1=2.

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I don't recognize half these symbols

>Prove to me that 1+1=2.
it depends on the circumstances. you can define mathematical structures for which 1+1 yields 0 for example.

also it depends on what you mean when you ask about 1 plus 1 yielding 2. one meaning can be the literal form of adding one and nother physical objects (e.g. an apple) yielding two apples as shown by experiment. but on an abstract level writing 1 + 1 just means to have an operator "+" which creates another symbol A out of two symbols a and a. the latter case depends on however you define the meaning of 1 and 2 and the operator "+".

this leads me to my conclusion:
your question is ill posed

2-1=1

Where's my prize

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but 1=2

Is this an excerpt from Principia Mathematica?

Lrn2formal-logic-mathematics fgt pls

Step Hyp Ref Expression
1 1on 6454 . . 3 ⊢ 1o ∈ On
2 cdaval 7764 . . 3 ⊢ ((1o ∈ On ∧ 1o ∈ On) → (1o +c 1o) = ((1o × {O}) ∪ (1o × {1o})))
3 1, 1, 2 mp2an 656 . 2 ⊢ (1o +c 1o) = ((1o × {O}) ∪ (1o × {1o}))
4 xp01disj 6463 . . 3 ⊢ ((1o × {O}) ∩ (1o × {1o})) = O
5 1 elexi 2772 . . . . 5 ⊢ 1o ∈ V
6 0ex 4124 . . . . 5 ⊢ O ∈ V
7 5, 6 xpsnen 6914 . . . 4 ⊢ (1o × {O}) ≈ 1o
8 5, 5 xpsnen 6914 . . . 4 ⊢ (1o × {1o}) ≈ 1o
9 pm54.43 7601 . . . 4 ⊢ (((1o × {O}) ≈ 1o ∧ (1o × {1o}) ≈ 1o) → (((1o × {O}) ∩ (1o × {1o})) = O ↔ ((1o × {O}) ∪ (1o × {1o})) ≈ 2o))
10 7, 8, 9 mp2an 656 . . 3 ⊢ (((1o × {O}) ∩ (1o × {1o})) = O ↔ ((1o × {O}) ∪ (1o × {1o})) ≈ 2o)
11 4, 10 mpbi 201 . 2 ⊢ ((1o × {O}) ∪ (1o × {1o})) ≈ 2o
12 3, 11 eqbrtri 4016 1 ⊢ (1o +c 1o) ≈ 2o

Proving 2+2=4 takes over 27,000 steps.

That's not the proof that 1+1=2. That theorem states that two sets of cardinality 1 are disjoint iff their union has cardinality 2.

that's literally what 1 + 1 = 2 means

further proof that all mathematicians should be killed

hm, yes. Quite.

I feel like a [math]brainlet[/math] after reading this thread

Don't. Foundations set autism is just mathematical masturbation.

Why?
Because bunch of autismos cant agree on a theorem?

"From this proof it will follow"
[math]once arithmetical addition has been defined[/math]
>once arithmetical addition has been defined
>once

We literally just made up math so we can do things. We're trying to prove something that we made up in the first place.

>I like purple
prove it
>alas, I cannot
Here's what we'll do, let's just make up some more stuff that proves the other stuff
Purple + like = LikesPurple
>it all makes sense now
No, you're wrong, now we need to prove THAT
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>now I finally understand
>that I like purple

See what I mean?

Yes, but finding the minimum amount of axioms you need to prove things is important. Otherwise you're just arbitrarily making shit up and a system is incoherent.

Yeah you're right. I was just thinking that in this specific scenario it doesn't make sense to try to prove 1+1=2, because we really just made it up on the spot. Unless you think otherwise? I'm open to others opinions.

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I disagree.