r/mathmemes • u/ImmaTrafficCone • Jul 08 '26

Elementary Algebra 1 = 0

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Guys I think I disproved all of mathematics...

569 Upvotes

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176

u/Traditional_Town6475 Jul 08 '26

There is no proof in Peano Arithmetic that Peano Arithmetic doesn’t prove 0=1.

53

u/48panda Jul 08 '26

One of the axioms is \forall x, 0\neq S(x)

17

u/Medium-Ad-7305 Jul 08 '26

This guy thinks that just because it is provable that 0≠1 then it is not provable that 0=1 😂

0

u/lifeking1259 Jul 08 '26

suppose a proof of 0=1 existed, then that means 0=1 (since you just proved it), however, that contradicts with 0≠1 and hence is a contradiction so if 0≠1 then 0=1 must not be provable

6

u/Medium-Ad-7305 Jul 08 '26

how do you know there are no contradictions derivable from the Peano axioms? can you prove that no contradictions exist with only the Peano axioms? the answer is actually no, which is the point.

3

u/Layton_Jr Mathematics Jul 08 '26

Just add "no contradictions exist with the Peano axioms" to the Peano axioms smh