We could have written = as "equals", + as "plus", $\exists$ as "thereExists" and so on. Supplemented with some brackets everything would be just as precise.
$$\exists x,y,z,n \in \mathbb{N}: n>2 \land x^n+y^n=z^n$$
could equally be written as:
ThereExists x,y,z,n from theNaturalNumbers suchThat
n isGreaterThan 2 and x toThePower n plus y toThePower n equals z toThePower n
What is the reason that we write these words as symbols (almost like a Chinese word system?)
Is it for brevity? Clarity? Can our visual system process it better?
Because not only do we have to learn the symbols, in order to understand it we have to say the real meaning in our heads.
If algebra and logic had been invented in Japan or China, might the symbols actually have just been the words themselves?
It almost seems like for each symbol there should be an equivalent word-phrase that it corresponds to that is accepted.
Best Answer
"Integral From a x squared Plus b Plus c To Infinity of a Times LeftParenthesis x Plus LeftParenthesis x Plus c RighParenthesis Over LeftParenthesis x Plus One RightParenthesis Differential x IsGreater Integral From a x squared Plus b Minus c To Infinity of a Times LeftParenthesis x Plus LeftParenthesis x Plus c RighParenthesis Over LeftParenthesis x Minus One RightParenthesis Differential x Implies Integral From a x squared Minus b Plus c To Infinity of a Times LeftParenthesis x Plus LeftParenthesis x Plus c RighParenthesis Over LeftParenthesis x Plus One RightParenthesis Differential x IsGreater Integral From a x squared Plus b Minus c To Infinity of a Times LeftParenthesis x Plus LeftParenthesis x Plus c RighParenthesis Over LeftParenthesis x Minus One RightParenthesis Differential x" ?
Quiz:
Do you recognize this one ?
Summation On j From 1 Upto N Of y Index k Times the Product On k From 1 And k NotEqual to j Upto N Of x Minus x Index k Over x Index j Minus x Index k.