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Pythagorean theorem (view source)
Revision as of 19:18, February 14, 2021
, 19:18, February 14, 2021→Conceptualization (cont'd)
Conditional sub-proof of indirect proof: Let's introduce a second hypothesis and see what follows from it.
Conditional sub-proof of indirect proof: Let's introduce a second hypothesis and see what follows from it.
:Simple assumption: One or more sets of ''two'' natural numbers, a pair ''n'' and ''o'', for example, exist that have a positive integral factor ''f'' apart from one and themselves and common to both of them.
:Simple assumption: One or more sets of ''two'' natural numbers, a pair ''n''<sub>1</sub> and ''n''<sub>2</sub>, for example, exist that have a positive integral factor ''f'' apart from one and themselves and common to both of them.
:Corollary to assumption: Through the definition of prime numbers such as described in the first "conceptualization" section, if any pair of positive integers ''n'' and ''o'' have an common integral factor ''f'' apart from one and themselves, they are not prime because they ''both'' have a non-prime type of positive integral factor; in fact it's the same one.
:Corollary to assumption: Through the definition of prime numbers such as described in the first "conceptualization" section, if any pair of positive integers ''n''<sub>1</sub> and ''n''<sub>2</sub> have an common integral factor ''f'' apart from one and themselves, they are not prime because they ''both'' have a non-prime type of positive integral factor; in fact it's the same one.
Conditional sub-proof to be proven: ''Assuming no pair of prime numbers can possess the qualities of the pair set with the described factor, no three lines having prime numbers as lengths can form a right triangle.''
Conditional sub-proof to be proven: ''Assuming no pair of prime numbers can possess the qualities of the pair set with the described factor, no three lines having prime numbers as lengths can form a right triangle.''
:(''l''<sub>1</sub><sup>2</sup> / ''h'') + (''l''<sub>2</sub><sup>2</sup> / ''h'') = ''h''
:(''l''<sub>1</sub><sup>2</sup> / ''h'') + (''l''<sub>2</sub><sup>2</sup> / ''h'') = ''h''
===Conceptualization (cont'd)===
The conceptualization of the simple assumption can be expressed as
:If (''n''<sub>1</sub> / ''f'') + (''n''<sub>2</sub> / ''f'') = ''n''<sub>3</sub> then ''n''<sub>1</sub> and ''n''<sub>2</sub> are not prime.
[[Category:Plane Geometry]]
[[Category:Plane Geometry]]
[[Category:Mathematics]]
[[Category:Mathematics]]
[[Category:Geometric Theorems]]
[[Category:Geometric Theorems]]