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felipec  unbelief  2yr ago (felipec.substack.com)   3599 thread views

2+2 = not what you think

felipec.substack.com

Changing someone's mind is very difficult, that's why I like puzzles most people get wrong: to try to open their mind. Challenging the claim that 2+2 is unequivocally 4 is one of my favorites to get people to reconsider what they think is true with 100% certainty.

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That's not how modular arithmetic works: 2+2=4 is still true, it's just that 4=0 mod 4, so 2+2=0 is also true.

Even if your example were true, that would just be notation confusion: The statement commonly meant by 2+2=4 is always true. So if I say 2+2=4 is always true, I'm correct, and if you say 2+2=? and the answer isn't 4 you're just communicating badly by omitting relevant information about the problem statement. In honest conversation this doesn't change anything.

That's not how modular arithmetic works: 2+2=4 is still true

There is no 4 in modulo 4, you are confusing the modulo operation with modular arithmetic, they are two different concepts that lead to the same result.

I'm not, neither of us was talking about the modulo operation (I was using mod 4 to denote I'm operating in the congruence class ring).

And the article about modular arithmetic agrees with me. Choice quote:

Each residue class modulo n may be represented by any one of its members

It may be represented that way, but they are not the same thing.

You yourself accepted here that 4 (sa) is not the same statement as 4 (mod 4).

So your claim that 4 (sa) = 0 (mod 4) is just plainly false.

It may be represented that way, but they are not the same thing.

4 and 0 are equivalent as representants of the residue class. If you can write down 2+2 where 2 refers to a residue class, the answer can be written down as 4.

your claim that 4 (sa) = 0 (mod 4)

How many times do I have to ask you to stop misquoting me?

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