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Just for fun, I've accepted a challenge to white in a form of a mathematical expression the expression "Not all is black and white". At first, I thought it will be easy, but now I am stuck. Here are some of the examples I tried:

¬∀xP(x)∈{#000000,#FFFFFF}

or ¬∀xP(x)=#000000∧¬∀xP(x)=#FFFFFF

or ¬∀x(P(x)=1∧P(x)=0)

or above combinations with addition of ∈ R so it would look like:

¬∀x∈R P(x)∈{#000000,#FFFFFF}

Just to break a daily routine :D

Thanks!

Blejzer
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    The sentence is ambiguous. Either $\neg (\forall x : (is-black(x) \wedge is-white(x)))$ or $\neg[(\forall x : is-black(x)) \wedge (\forall x : is-white(x))]$ – David Lui Mar 06 '23 at 10:11
  • Yes it is (sentence)! Great suggestion! I would prefer more universal expression, avoiding English or any other language for that matter, except math exp. – Blejzer Mar 06 '23 at 10:42
  • Why would you "prefer more universal expression, avoiding English"? Real mathematics tends to use as much plain language (English or French or Russian or whatever) as possible, falling back on notation only when it is necessary to clearly convey the ideas the author wants to convey. Writing things in notation just for the sake of writing them in notation tends to make it harder to actually understand what is intended. – Xander Henderson Mar 06 '23 at 10:51
  • If I wanted to convey this sentence unambiguously in a mathematical text, I would first try to figure out what I really mean by the phrase, and then use plain English to describe that. In this case, something like "Not everything is just black and white. There can be shades of grey." – Xander Henderson Mar 06 '23 at 10:54

1 Answers1

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Just adding a few more to the mix:

$E=\{\mathbb{\#} 000000,\mathbb{\#}FFFFFF\}, E^{C}\neq \emptyset$

or

$A=\{A,B,C,\dots,X,Y,Z\}, \sigma(A)=B, \sigma(B)=c,\dots,\sigma(Z)=A\Rightarrow \sigma^{-1}(\text{O})\sigma^{-1}(\text{p})\sigma^{-1}(\text{u})\dots\sigma^{-1}(\text{f})=\text{NotAllIsBlackAndWhite}$

MathematicianByMistake
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