What is proof? (Part 2) | Intro to Math Structures VS1.3
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- Опубліковано 15 вер 2024
- We pick up where we left off (after a slight digression) to talk about "what is proof?". This time around we'll look at an example of a constructive proof. Here we prove the Pythagorean theorem constructively using a classic geometric argument, and then give some exercises that will be covered in shorts format later on.
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There is something so satisfying about the chalk you use, or perhaps that's just the geek in me haha. Well-made video, cheers!
Thanks 😄 I guess the 99¢ boxes of chalk I got at Michael’s on a whim several years ago hold up 😅
Great Video as always, thanks a lot!
Thanks Wilbert glad you enjoyed it!
You don't need to slide anything in the geometric construction. The 4 right triangles cover an area of 4×(1/2)×a×b=2ab and the total area of the square is (a+b)^2 = a^2 + 2ab + b^2 and also the total area of the square is c^2 + (area of triangles) = c^2 + 2ab. Thus a^2 + b^2 = c^2.
If you want to stay solely in the realm of geometry and avoid algebra then sliding around is necessary.
"If you want to stay solely in the realm of geometry and avoid algebra then sliding around is necessary."
Hello, from a fellow Carleton math major!
Hello!
Let V := {n in N | (n=1) or (n=0 and ConT)} where ConT claims the arithmetized consistency of the theory you're working in. V is an inhabited subset of {0,1}. Assuming the least number principle (or well-ordering of N) there "exists" a least member of V. But what is it!? --- Proof by wishful thinking and empty promises. So just like my Valentine's day.
every time I read one of these comments I google things and learn more about intuitionistic logical
structures
@@CHALKND It's on my mind as I made a video about the line of transition to the classical framework two weeks ago. This could help a bit.
Although I'm currently looking into catch up basic approximation theory for the continuous functions on R, which I suppose you're closer to.