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Response to intrepidity (Reply #14)

Thu Mar 4, 2021, 08:17 PM

15. The point is proving a specific case doesn't prove the generality.

If I claim that every prime can be written as a sum of two squares of integers, and then "prove" it by saying: 13 = 2^2 + 3^2
does that really work?

No, it just shows that 13 is the sum of two squares. But if you try 7, you get an example that doesn't work.

The demonstration above shows that a particular right triangle satisfies the equation in Pythagoras' Theorem, but the Theorem claims that the result will hold for ANY right triangle.

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soothsayer Mar 2021 OP
keithbvadu2 Mar 2021 #1
Clash City Rocker Mar 2021 #2
eppur_se_muova Mar 2021 #3
intrepidity Mar 2021 #4
eppur_se_muova Mar 2021 #5
intrepidity Mar 2021 #6
muriel_volestrangler Mar 2021 #7
intrepidity Mar 2021 #8
muriel_volestrangler Mar 2021 #9
intrepidity Mar 2021 #10
muriel_volestrangler Mar 2021 #11
intrepidity Mar 2021 #12
muriel_volestrangler Mar 2021 #13
intrepidity Mar 2021 #14
LineLineLineLineLineLineLineLineLineLineNew Reply The point is proving a specific case doesn't prove the generality.
Dr. Strange Mar 2021 #15
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