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pyesetzAt MathOverflow.
I understand almost none of these false-belief descriptions, hence I believe myself to be immune to these misconceptions. I most certainly do not believe that "The field of p-adic numbers has characteristic p" because I do not believe that I know what p-adic numbers are. In a similar vein, it cannot be said that I have been fooled into thinking that "If A⊗B=0 for abelian groups A,B, then either A=0 or B=0." While I do happen to know that it is false to say that "ℵ₁ is defined as 2ℵ₀ or |ℝ|", this is only because there are so many Unicode characters in that statement, so I recently had a non-math reason to study it.
Being an educated person, of course I remember from junior high that "0.999... = 1". I do not believe that "If A implies B then B implies A", nor that "If you play the casino patiently and carefully you will win in the long run", nor that "It is known that quantum computers can solve NP complete problems in polynomial time."
Okay, perhaps I do believe that "if you hold a cube along a main diagonal, the remaining vertices all lie on a plane." Nobody's perfect! (That's an octahedron, which is the dual of the cube.)
Personally, I prefer to believe the (false to mathematicians) statement that "an event which may occur has positive probability", even though this is not true for infinite probability spaces, because I don't believe in infinity. I also decline to believe that "Euclid's proof is not not by contradiction", nor that "It depends on personal opinion and interpretation what a proof by contradiction is..." The claim that "It is more important to be correct than to be understood" really shouldn't be plausible. As for "topologists need a sit-down about the facts of life in life, where they are told how unfortunate their notation is...", I am only too willing to believe that this is so, although it might very well not be, for all I know.
I agree with these commenters that "It's things like this that help me to remember how very little I know about mathematics." and "It's kind of humbling to know that I can't understand any of that."
I understand almost none of these false-belief descriptions, hence I believe myself to be immune to these misconceptions. I most certainly do not believe that "The field of p-adic numbers has characteristic p" because I do not believe that I know what p-adic numbers are. In a similar vein, it cannot be said that I have been fooled into thinking that "If A⊗B=0 for abelian groups A,B, then either A=0 or B=0." While I do happen to know that it is false to say that "ℵ₁ is defined as 2ℵ₀ or |ℝ|", this is only because there are so many Unicode characters in that statement, so I recently had a non-math reason to study it.
Being an educated person, of course I remember from junior high that "0.999... = 1". I do not believe that "If A implies B then B implies A", nor that "If you play the casino patiently and carefully you will win in the long run", nor that "It is known that quantum computers can solve NP complete problems in polynomial time."
Okay, perhaps I do believe that "if you hold a cube along a main diagonal, the remaining vertices all lie on a plane." Nobody's perfect! (That's an octahedron, which is the dual of the cube.)
Personally, I prefer to believe the (false to mathematicians) statement that "an event which may occur has positive probability", even though this is not true for infinite probability spaces, because I don't believe in infinity. I also decline to believe that "Euclid's proof is not not by contradiction", nor that "It depends on personal opinion and interpretation what a proof by contradiction is..." The claim that "It is more important to be correct than to be understood" really shouldn't be plausible. As for "topologists need a sit-down about the facts of life in life, where they are told how unfortunate their notation is...", I am only too willing to believe that this is so, although it might very well not be, for all I know.
I agree with these commenters that "It's things like this that help me to remember how very little I know about mathematics." and "It's kind of humbling to know that I can't understand any of that."
