Editing 704: Principle of Explosion

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Cueball then proceeds to misinterpret (perhaps intentionally) that you can derive any ''fact'' about the physical world. His formula of {{w|propositional logic}} in the third panel reads "'''P''' and not '''P'''", where '''∧''' is the formal logic symbol for "and" and '''<sup>¬</sup>''' is the symbol for "not". '''P''' stands for a proposition. As "'''P''' and not '''P'''" is shorthand for "'''P''' is both true and false", this forms a contradiction from which the principle of explosion can begin. Humorously and to his friend's bewilderment he then successfully manages to 'derive' the phone number for his friend's mom.  
 
Cueball then proceeds to misinterpret (perhaps intentionally) that you can derive any ''fact'' about the physical world. His formula of {{w|propositional logic}} in the third panel reads "'''P''' and not '''P'''", where '''∧''' is the formal logic symbol for "and" and '''<sup>¬</sup>''' is the symbol for "not". '''P''' stands for a proposition. As "'''P''' and not '''P'''" is shorthand for "'''P''' is both true and false", this forms a contradiction from which the principle of explosion can begin. Humorously and to his friend's bewilderment he then successfully manages to 'derive' the phone number for his friend's mom.  
  
:'''An example from math''': If you assume that √2 is a rational number, you can 'prove' things that are obviously false, such as the fact that some numbers must be both even and odd. Consequently, you can draw the conclusion that √2 must be an irrational number (provided such a thing exists at all! - luckily, it does and obeys the same calculation rules as for rational numbers; this is how {{w|proof by contradiction}} works.)
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:'''An example from math''': If you assume that √2 is a rational number, you can 'prove' things that are obviously false, such as the fact that some numbers must be both even and odd. Consequently, you can draw the conclusion that √2 must be an irrational number (provided such a thing exists at all! - luckily, it does and obeys the same calculation rules as for rational numbers; this is how {{w|proof by contradiction}} works.))
  
 
:This can be seen in a {{w|Truth Table}}:
 
:This can be seen in a {{w|Truth Table}}:

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