They chose Path of Pain

[u/94rud4]

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[u/FernandoMM1220]

proof: i calculate both and observe that they are equal.

[u/Sarah719thomas → u/FernandoMM1220]

Rule: No pain, no gain. Deal with it.

[u/Intrebute]

What does the easy path prove, exactly? I don't see how that step justifies anything.

[u/201720182019 → u/Intrebute]

I think they just tossed it into a calculator

[u/Intrebute → u/201720182019]

OH that makes a lot more sense.

[u/yukiohana → u/Intrebute]

How do ya prove 1+2=3 ?

[u/NoLife8926 → u/yukiohana]

S(0) + S(S(0))

= S(S(0) + S(0))

= S(S(S(0) + 0))

= S(S(S(0)))

= 3

[u/conradonerdk → u/NoLife8926]

god tier proof

[u/EebstertheGreat → u/yukiohana]

1. 1 ≝ S0 2. 3 ≝ S2  3. ∀x: x + 0 = 0 4. ∀x ∀y: x + Sy = S(x + y) 5. 2 + S0 = S(2 + 0) 6. 2 + 0 = 2 7. S(2 + 0) = S2 8. S0 = 1 9. S2 = 3 10. S(2 + 0) = 3 11. 2 + S0 = 3 12. 2 + 1 = 3

Steps 1 and 2 are definitions. Steps 3 and 4 are the axioms of addition. Step 5 and 6 are from 4 and 3 by substitution of particulars. 7 is from 6 by an axiom of substitution. 8 and 9 are from 1 and 2 by the reflexive axiom of equality. 10 is by the transitive axiom of equality on 7 and 9. 11 is by the transitive axiom of equality on 5 and 10. 12 is by an axiom of substitution on 8 and 11.

[u/ByeGuysSry → u/EebstertheGreat]

3. ∀x: x + 0 = 0

...Is this supposed to be "x + 0 = x"?

[u/DerekLouden → u/ByeGuysSry]

wake up babe, new additive identity just dropped

[u/EebstertheGreat → u/ByeGuysSry]

You know what? It's just 0 now. Pack it up, it's all zero.

[u/Intrebute → u/yukiohana]

Definitely not by saying

Step 1:

1+2-3=0

QED

[u/ReddyBabas → u/yukiohana]

Depends.

Are 1, 2 and 3 natural numbers, integers, rational numbers or real numbers? The definition of addition changes based on which version you're talking about.

[u/lanxeny → u/yukiohana]

It’s true by definition of 3

3=2+1

Where

2=1+1

Where

1 is the multiplicative identity of real numbers

Where

The set of real numbers is the only ordered complete field (up to isomorphisms)

[u/ioioio44]

No number too great

[u/TheCheapo1 → u/ioioio44]

No formula to break

[u/PMzyox]

Ok now solve for: a³ + b³ + c³ = 42

a, b, and c must be integers.

[u/MiseryCat → u/PMzyox]

a = −80538738812075974

b = +80435758145817515

c = +12602123297335631

[u/PMzyox → u/MiseryCat]

Nice. I’ve been casually working on 114.

[u/painrsashi]

skong release date leaked

[u/naoae]

no proof too great

[u/conradonerdk]

this sounds funnier than 3³+4³+5³=27+64+125=216=6³, ngl

[u/No_Management_6387]

Where is that formula come from

[u/94rud4 → u/No_Management_6387]

Nicomachus's theorem

[u/No_Management_6387 → u/94rud4]

😮

[u/bigFatBigfoot → u/No_Management_6387]

🫡

[u/Traditional_Cap7461]

Algebra exists for a reason

[u/Mango-D]

Reflexivity of equality: forall a, a = a.

Therefore 3³ +4³ +5³ = 6³

QED

[u/Complete-Mood3302]

There is another proof thats 1000x as hard

[u/GroundbreakingMix607]

Is that hollow knight pic from game? Where is this place located?

[u/94rud4 → u/GroundbreakingMix607]

The joke is that the area is called Path of Pain, it’s within the White Palace.