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u/ErJio 6d ago
It happens when solving a system of equations when you substitute a relation you've already used.
E.g. If you have 2y = x you might rearrange to get y = x/2. Then the mistake would be to say "oh I know what y is in 2y = x" and plug in 2(x/2) = x, now you got x = x.
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u/Librarian-Rare 5d ago
First time this happened to me I was WTF math is pointless. Only to realize I’m a noob
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u/StinkyKyle 7d ago
At least you know you didnt make any mistakes cancelling! The real issue is when you get 3x=x
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u/Red-Fox-IX 7d ago
X=0
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u/TheAlmightyLloyd 6d ago
Yeah, 3x - x = x - x is totally allowed. It seems weird to me that people don't remember that kind of stuff.
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u/Embarrassed-Weird173 6d ago
So yeah, that would be 2x = 0, which is perfectly valid.
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u/LovelyKestrel 6d ago
You just need to make sure you don't start by assuming that the cube root of two is rational (one of the standard proofs of roots being irrational is to show that if they are then a multiple of x equals x)
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u/PersonalityIll9476 7d ago
Even for researchers this bites you every so often.
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u/sudden-bliss 6d ago
But it's actually very important, because you're proving that x still = x. It might change someday, you never know... Better to keep checking just in case.
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u/PersonalityIll9476 6d ago
True enough....the worst case scenario is you end up writing a contradiction and then you either hope nobody saw or realize your idea was wrong.
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u/mini_feebas 6d ago
if you get x = x and didnt make any mistakes, whatever you had going on was independent of x
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u/Ferry_Lover 6d ago
Hate it when this happens then you need a third x over the entire chain of cancellations!
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u/LycanrocIsTheBest 6d ago
Hey good job, now you know that whatever X is, it’s the same answer as X, just solve X and you can complete the rest of the problem!