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Sagot :
Answer:
indeed it is
Explanation:
Whitehead and Russell's Principia Mathematica is famous for taking a thousand pages to prove that 1+1=2. Of course, it proves a lot of other stuff, too. If they had wanted to prove only that 1+1=2, it would probably have taken only half as much space.
Principia Mathematica is an odd book, worth looking into from a historical point of view as well as a mathematical one. It was written around 1910, and mathematical logic was still then in its infancy, fresh from the transformation worked on it by Peano and Frege. The notation is somewhat obscure, because mathematical notation has evolved substantially since then. And many of the simple techniques that we now take for granted are absent. Like a poorly-written computer program, a lot of Principia Mathematica's bulk is repeated code, separate sections that say essentially the same things, because the authors haven't yet learned the techniques that would allow the sections to be combined into one.
For example, section ∗22, "Calculus of Classes", begins by defining the subset relation (∗22.01), and the operations of set union and set intersection (∗22.02 and .03), the complement of a set (∗22.04), and the difference of two sets (∗22.05). It then proves the commutativity and associativity of set union and set intersection (∗22.51, .52, .57, and .7), various properties like α∩α=α" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">α∩α=αα∩α=α (∗22.5) and the like, working up to theorems like ∗22.92: α⊂β→α∪(β−α)" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">α⊂β→α∪(β−α)α⊂β→α∪(β−α).
Section ∗23 is "Calculus of Relations" and begins in almost exactly the same way, defining the subrelation relation (∗23.01), and the operations of relational union and intersection (∗23.02 and .03), the complement of a relation (∗23.04), and the difference of two relations (∗23.05). It later proves the commutativity and associativity of relational union and intersection (∗23.51, .52, .57, and .7), various properties like α∩˙α=α" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">α∩˙α=αα∩˙α=α (∗22.5) and the like, working up to theorems like ∗23.92: α⊂˙β→α∪˙(β−˙α)" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">α⊂˙β→α∪˙(β−˙α)α⊂˙β→α∪˙(β−˙α.
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