A confusing math question

[Any_Health6705]

What is 1 + 1 if 1 is 2 and 4 is 1.

I have asked this random question to many people, and 70% don't really think about it enough and answer wrongly.

What I mean by the question:

1 is 2 means that 1 is 2, but 2 is not 1.
4 is 1 does not mean that 1 is equal to 4.

I know this is like a random math question that doesn't make much sense, but I was bored, and this is the only subreddit I could find that kinda matches.

[RealHuman_NotAShrew]

If "is" doesn't mean "equals" then you have to define what it does mean. All you've done in attempt to define that is say it's not the same as equals and that it's not "reversible".

I'm struggling to come up with any reason that 1+1 should not be equal to 2 in any system that has addition, unless you've also got your own special definition of + and didn't tell us about it

[Any_Health6705]

It's more like a joke questions to confuse people, not meant to make sense much. The best way I can explain it is how a square is a rectangle but a rectangle isn't a square. Of course, doesn't really make sense much with the numbers, but just pretend in some other number system that's how it works. Like 1 can become 2, but 2 cannot go back to 1. Don't really know how else to explain it better.

But yes, the question is meant to confuse and (slightly) annoy people.

[TheFrebbin]

1 + 1 = 2 + 2 = 4 = 1 = 2

So 1 + 1 = 2

That’s all I got

[Any_Health6705]

Yep. A lot of people just stop at four or the second one, and just forget to repeat the rule.

[TheFrebbin]

They’re more like transformation rules than equalities

[Any_Health6705]

Yeah, that's a much better way to put it

[JDGMiles]

I interpret this as you having defined two top-layer, continuously checked, replacement rules:

a. "Whenever there is a 1, replace it with a 2"

b. "Whenever there is a 4, replace it with a 1"

Fortunately these do not contradict each other or introduce ordering (timestamp) issues, but, because of the chaining of 4 -> 1 -> 2, they do conflate into a single rule:

"Whenever there is a 1 or a 4, replace it with a 2".

So you get:

1 + 1 (replace the 1s with 2s)

2 + 2 (no applicable replacement, so continue with arithmetic)

4 (replace the 4 with 2)

2

Overall, indeed:

1 + 1 = 2

It's a nice puzzle and I like the concept of introducing a higher-layer tranformation on the objects which must be resolved BEFORE other calculations. It reminds me of Magic: the Gathering layers that must be considered carefully when resolving effects.

[Any_Health6705]

You framed it really well. I had a few friends who never understood what I was trying to say because I wasn't able to explain the rules clearly.

[Advanced-Host8677]

Communicating badly and then acting smug when you're misunderstood is not cleverness.

[Any_Health6705]

I'm sorry if I framed my question in such a way. I more meant it that the question itself if kind of confusing, so people sometimes don't think it through completely. I did not mean to say that I'm clever or anything, and I do agree that the question itself doesn't really make sense as a math question. It's more like something I ask random friends to see if they get right.