3 ms·
> One of the reasons that the proof of 2 + 2 = 4 is so long is that 2 and 4 are complex numbers—i.e. we are really proving (2+0i) + (2+0i) = (4+0i) Yeah, this
by HL33tibCe7 4y ago
> One of the reasons that the proof of 2 + 2 = 4 is so long is that 2 and 4 are complex numbers—i.e. we are really proving (2+0i) + (2+0i) = (4+0i)
Yeah, this is why
- lisper 4y agoRight. That seems like an unnecessary detour to me.
- Natsu 4y agoIt's necessary to go down to the level of axioms and do one step at a time. It's obviously not needed for us to see that this proof is correct. A human proof would probably not generally go beyond something like: 2+2=4 1+1+1+1 = 1+1+1+1 // Substitute the definitions of 2 (1+1) and 4 (1+1+1+1)
- lisper 4y agoExcept that 4 is not 1+1+1+1, it's the successor of 3, which is the successor of 2 which is the successor of 1 which is the successor of 0. So you'd have to show that: S(S(0)) + S(S(0)) = S(S(S(S(0)))) and that is non-trivial. (But it's not 26,000 steps either.)
- Natsu 4y agoI'm assuming those steps in the definitions of 2 and 4, but you're right that this is part of why it gets so tedious.
- WastingMyTime89 4y agoIt is trivial in most axiomatic systems. It’s directly linked to how + is defined and will mostly boil down to applying it. The 26000 steps proof is extremely convoluted.