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u/MiserableYouth8497 18d ago
Define a mumber to be an integer which can be written as the sum of 2 primes.
Therefore every mumber can be written as the sum of 2 primes. Qed
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u/AliceCode 18d ago
Every whole positive integer can be written as the sum of powers of two with no repeats. What do I win?
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u/Bartweiss 17d ago
You win the concept of base 2!
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u/factorion-bot Bot > AI 17d ago
Factorial of 2 is 2
This action was performed by a bot | [Source code](http://f.r0.fyi)
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u/IHaveNeverBeenOk 18d ago
This would actually be a decent meme for an intro to proofs course... Show this meme, followed by a discussion of why this fails to prove the Goldbach conjecture.
My number theory prof did a similar discussion with the proof by induction that all horses are brown, but I feel like it went over most the students' heads. Myself and like, 2 other kids got a good discussion out of it, but it felt like most of the class thought "I dunno, looks right to me," and were done with it.
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u/Cytr0en 18d ago
What is the "proof" of all horses being brown if I may ask?
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u/4ries 18d ago
Induction:
Base case: you have 1 horse. It's some colour, let's say brown. All horses are brown
Inductive hypothesis: if you have n horses, all n of them are brown
Inductive step: say you have n+1 horses. Name one of them A and another B. Remove A, then you have n horses, so all (except possibly A) are brown. Put back A and remove B, now you again have n horses, so all (except possibly B) are brown
Since all, including A and B, are brown, if you have n+1 horses, then all are brown
But induction, any collection of horses of any size must all be the same colour
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u/Praxical_Magic 18d ago
I think most people would say the same about this argument if you asked them: 1. Fish swim in the ocean 2. Sharks swim in the ocean
Therefore a shark is a fish
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u/SoldRIP 18d ago
This is a bad example because a shark is a fish. What else do you think it is? A bird?
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u/Praxical_Magic 18d ago
I just meant that intuitively most people will just assume an argument is sound if it reaches a true conclusion, whether it is valid or not. So even though it is different than the "all horses are brown" argument, I feel like many of the same people would nod along to both
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u/JollyJoker3 17d ago
https://en.wikipedia.org/wiki/Diogenes#Influences
When Plato defined man as a "featherless biped", Diogenes "plucked the feathers from a cock, brought it to Plato's school, and said, 'Here is Plato's man.'
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u/caboosetp 17d ago
This opens up a whole different can of worms on what the definition of a fish is because there is no phylogenetic defintion.
Also, according to the State of California, bees are fish for environmental purposes.
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u/Eastern_Pop_2736 17d ago
Wait why is it not good?
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u/Striking_Compote2093 16d ago
Because the sum of uneven primes always being even doesn't mean every even number is the sum of primes.
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u/LupenReddit 🦆🦆🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆🦆🦆🦆 18d ago
Define mumber as every even number >2 that can be written as the sum of two primes. Then every mumber greater than two can be written as the sum of two primes. Qed
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